WO2016032432A1 - Method and system for heterodyned fluorescence tomography - Google Patents

Abstract

A solid state detection system includes a degenerate photo-parametric amplifier (PPA), wherein the PPA comprises a photo diode, and a periodically pulsed light source, wherein the photo-parametric amplifier (PPA) is synchronized to the pulsed light source with a phase locked loop that generates a pump waveform for the PPA at twice the frequency of the excitation pulse rate.

Description

METHOD AND SYSTEM FOR HETERODYNED FLUORESCENCE TOMOGRAPHY

BACKGROUND

Field of the Invention

[001] The present invention relates to fluorescence tomography, and particularly to a novel fluorescence tomography modality referred to herein as "heterodyned fluorescence tomography" or "HFT"

Context of the Invention

[002] Tomography of various kinds have been developed as valuable tools for a non-invasive imaging within a body of material, particularly as tools for imaging within a living organism such as the human body for diagnosis and bio-medical research. In tomography, images are produced by measurements of energy waves of one type or another that have passed through at least a portion of the body of material to be imaged and the measurements are employed to compute an image representative of the interior of the body. The energy waves may be electromagnetic waves that pass through the body and are measured for intensity when they exit the body, as in the case of X-rays in computerized axial tomography, or a "CAT scan"; they may be electromagnetic waves induced within the body and measured for intensity when they exit the body, as in the case of radio waves in magnetic resonance imaging, or "MRI"; or they may be acoustical waves that pass into the body and are scattered back to a device outside the body which measures the intensity of waves scattered back from a particular depth within the body, as in ultrasound imaging.

[003] Three particular considerations that bear on whether a type of tomography is appropriate or not are the depth within the body at which useful images can be obtained, the extent to which the waves are likely to damage the body of material, and the resolution of the images that can be obtained. For example, in a CAT scan X-rays are used in medical diagnoses to obtain deep penetration of the human body and high resolution; at the same time, the extent to which CAT scans should be used is limited by the probability that X-rays, which have high energy, will cause serious damage to the DNA of living cells. As another example, ultrasound employs a much lower energy acoustical wave that does not present a known danger of DNA damage and has found valuable application in imaging larger features within the human body that do not require the high resolution that is obtained by higher energy waves. Other considerations may be involved as well, depending on the nature of the material and the purpose of the methodology.

[004] Electromagnetic waves of intermediate energy commonly, but imprecisely, known as "light waves", whether visible or not, offer the potential for tomography with good resolution and a low probability of DNA or other cellular damage in organisms. For example, in biomedical applications of optical coherence tomography, or "OCT", coherent light waves typically having near infrared energy are launched into living tissue and the backscattered energy is allowed to interfere with the source so that, because of the short coherence length of the waves, the measured intensity for a given phase delay is representative of the backscattering at a given depth in the tissue. An image of a volume within the object may be produced by scanning laterally over that volume while collecting interference intensity data. This technique provides good resolution for tissue density based on associated variations in the index of refraction of the tissue and is able to image tissue morphology, but it does so without any molecular specificity.

[005] Confocal microscopy employs the idea of using the objective of a scanning microscope not only to produce an image of the interior of an object, but to project the image of a light source into, and illuminate only the focal point within, the object. That improves resolution by reducing the detection of scattering from other points within the object. An image of a volume within the object may be produced by scanning over that volume while collecting back scattered intensity data. Together with the use of selected fluorophores that attach to particular molecules, confocal microscopy can also be made molecule specific. However, the effective depth of confocal microscopy is only about 100 μιη, while OCT can resolve structures as deep as about 400 μιη, into the material due to the greater random backscatter rejection capability of this interferometry method.

[006] The molecular specificity provided by fluorescent imaging enables significant biomedical research capabilities that cannot be achieved with measurements of mere backscattered light or interference intensity. However, the depth to which fluorescent imaging can penetrate a tissue has previously fallen far short of the depth to which OCT imaging can penetrate. [007] Since tissue pathologies of interest to physicians and researchers often lie deeper in the tissue than 400μηι₅ it has become desirable to develop additional new imaging modalities that employ energy waves that are unlikely to cause DNA damage yet enable high resolution images to be obtained at penetration depths greater than 400μπι.

BRIEF DESCRIPTION OF THE DRAWINGS

[008] Figure 1 A is a schematic diagram of a prior art optical coherence tomography system using a Michelson interferometer.

[009] Figure IB is a schematic diagram of a prior art optical coherence tomography system using a Mach-Zehnder interferometer.

[010] Figure 1C is a schematic diagram of a hypothetical optical coherence tomography system using a Mach-Zehnder interferometer, a fluorescent screen as an interference medium and a fluorescent light detector.

[011] Figure ID is a schematic diagram of an HFT system according to the present invention.

[012] Figure 2 is a plot of elliptical curves associated with OCT and hyperbolic curves associated with HFT.

[013] Figure 3 is a detailed schematic diagram of a single-objective HFT system.

[014] Figure 4 is a diagram of the results of a simulation of a single-objective HFT system in which the back aperture of the objective lens is divided into central and surrounding annular zones illuminated by slightly different frequencies so as to cause a continuously changing relative phase between the respective wave fronts.

[015] Figure 5A shows the magnitude and phase point spread functions of a simulated single- objective HFT system in which the back aperture of the objective lens is divided into a central and surrounding annular zones illuminated by slightly different frequencies so as to cause a continuously changing relative phase between the respective wave fronts.

[016] Figure 5B shows the magnitude and phase point spread functions of a simulated single- objective HFT system in which the back aperture of the objective lens is divided into two semicircular zones illuminated by slightly different frequencies so as to cause a continuously changing relative phase between the respective wave fronts.

[017] Figure 5C shows the magnitude and phase point spread functions of a simulated single- objective HFT system in which the back aperture of the objective lens is divided into two adjacent circular zones illuminated by slightly different frequencies so as to cause a continuously changing relative phase between the respective wave fronts.

[018] Figure 6 shows the measured photo multiplier tube current, magnitude point spread function and phase point spread function for an experimental HFT system according to the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Overview of the Disclosure

[019] HFT is a new imaging modality that extends the capabilities of microscopy to penetration depths comparable to OCT. Increasing the ability to image molecules via fluorescence microscopy about 10 times deeper into biological tissues is a significant advance of the state of the art of molecular imaging. In particular, HFT enables research that is currently not practical or very difficult, for example in- vivo tracking of stems cells, and potentially enables medical diagnosis of conditions earlier than currently possible.

[020] This disclosure is directed to a practical and versatile HFT scanner that can be deployed in a bio-medical laboratory to solve real problems. For example, with a scan depth of over 1 mm it will be possible to track cells in small organisms and embryos. It is a molecular imaging technology that is compatible with minimally invasive procedures, particularly to enable in-vivo, real-time, optical pathology. This may be used to determine the health of tissue during surgery without the need of extracting biopsy samples and analyzing them in a pathology laboratory, so as to improve cancer removal surgery. Theory of Operation

[021] The theory of operation of heterodyned fluorescence tomography (HFT) is explained in part herein by comparison of HFT to optical coherence tomography, OCT, as illustrated by Figs 1A, IB, 1C and ID.

[022] Turning first to the schematic diagram of an OCT system in Fig. 1 A, a typical OCT system 10 employs a Michelson interferometer having a coherent light source 12 generating light at source wavelength K_s, a beam splitter 14, a reference mirror 16, and a detector 18 sensitive to the source wavelength λ₅. Light from the source 12, having a relatively short coherence length, travels along path 20 to the beam splitter 14 where it is split into two paths, path 22 and path 24. Light along path 22 is directed to a sample 26 to be imaged and light along path 24 is directed to the reference mirror 16. The light directed to sample 26 is scattered back along path 22 to the beam splitter 14, and light directed to the reference mirror 16 is reflected back along path 24 to the beam splitter 14, where the light scattered by the sample and the light reflected by the mirror are combined and directed along path 28 to the detector 18. As is well understood in the art, when the optical path lengths of the path 22 and path 24 are within the light coherence length of one another interference will occur at detector 18, which produces a signal representative of the degree of such interference. By moving the reference mirror back and forth as shown by arrow 17 so as to vary the path length 24, the intensity of light scattered at corresponding depths within the sample 26 can be measured by the intensity of the interference detector 18.

[023] Similarly, as shown in Fig. IB an OCT system 30 could employ a Mach-Zehnder interferometer. In this case light from the coherent light source travelling along path 20 encounters a first beam splitter 32 where it is split into two paths, path 34 and path 36. Light along path 34 is directed to sample 26 and light along path 36 to a reference mirror 38, which reflects the light along path 40 to a second beam splitter 42, which passes that light there through and along path 44 to detector 18. (The reference mirror preferably is actually a mirror system that can vary the optical path length, as will be understood by a person having skill in the art.) In this case, light scattered by the sample 26 travels along path 46 to beam splitter 42, where it is reflected along path 44 and mixed with light from reference mirror 28 at the detector 18. While this illustrates the use of a Mach-Zehnder interferometer in OCT, that the light incident on and scattered from the sample 26 travel along different paths in this system means that it is not compatible with a confocal scanner as is ordinarily used in an OCT system of the type illustrated by Fig. 1 A.

[024] In Fig. 1C a hypothetical OCT system 50 uses the Mach-Zehnder configuration, but the second beam splitter 42 in Fig. IB is replaced in system 50 with a fluorescent screen 52. If the two paths 34, 46 and 36, 40 are within the coherence length of one another, then the two respective wavefronts will produce an interference pattern on the screen 52, manifested by light produced at the fluorescence wavelength \_f of the screen. In this case, a detector 54 is provided that is sensitive to the fluorescence wavelength _f, but not necessarily to the source wavelength λ₅. The gratuitous introduction of fluorescence in system 50 does not change the operating principle: the interference could be observed directly with, for example, a CCD array camera or a photographic plate in place of the fluorescent screen, or indirectly by observing the fluorescent light from the screen 52 either with the naked eye or the detector 54, depending on _f. In any case, the observed signal is proportional to the square of the sum of the two incident

electromagnetic waves arriving at the position of the fluorescence screen 52 along paths 46 and 40 respectively. This hypothetical system 50, which may offer an advantage in some

application, mainly sets the stage for understanding heterodyned fluorescence tomography.

[025] Turning now to Fig. ID an illustrative HFT system 60 also uses a Mach-Zehnder interferometer, but light travelling along path 34 encounters a second reference mirror 62, which reflects the source light along path 64, where it mixes with source light from path 40 within the sample 26, which is located where the fluorescent screen 52 is located in system 50. Thus, in this case, the sample 26 is also the interference detector. More precisely, the sample includes fluorophores and those fluorophores serve as detectors of the interference between the source light wave-front arriving from path 64 and the source light wave-front arriving from path 40, respectively. The fluorescent molecules within the sample 26 are excited by the coherent sum of the two wave-fronts and act as square-law detectors that produce an interference signal S< at wavelength X_f. The interference signal S, is received by a fluorescent light detector 66, which is preferably blind to the source light at wavelength λ₅.

[026] Interferometers compare optical path lengths. However, there is a difference between HFT and OCT in that HFT senses the optical path difference while OCT senses the round-trip optical path length. This provides advantages with HFT in some applications over OCT as described hereafter.

[027] Referring again to the Mach-Zehnder OCT configuration of Figure IB, the first beam splitter 32, where the beam is split, is essentially the location of the emitter and the second beam splitter 42, where the light is recombined, is essentially the location of the detector. Any scatterer that is located on an elliptical shell whose two focal points correspond to the locations of the first beam splitter 32 and the second beam splitter 42, respectively, will produce the same signal. This is illustrated by focal points 70 and 72, and ellipsoids 74, for example, in Fig. 2. However, in the case of the Michelson OCT configuration of Fig. 1A, the ellipsoid degenerates to a sphere with the center on the beam splitter. In the latter configuration, OCT can sense depth (Z), but only depth, while lateral resolution (X/Y) depends on a scanner.

[028] In contrast, referring again to the HFT shown by Fig. ID, the first reflective mirror 38 and the second reflective mirror 62 are both essentially emitters and the sample itself is the detector. All fluorophores that are located on hyperbolic shells that are defined by focal points located at mirrors 38 and 62 will produce the same signal. In other words, any point within the sample volume that has the same distance difference from mirror 38 and mirror 62 will generate the same signal. This relation is also illustrated in Fig. 2, where the points 70 and 72 correspond to the locations of the focal points, that is, the locations of the mirrors 38 and 62, and lines 76, for example, correspond to the hyperboloids. Consequently, HFT has good lateral (X Y) resolution but cannot resolve depth (Z) along the line of symmetry. However, using multiple acquisition steps with different emitter pairs, for example different positions of the mirrors 38 and 62, and applying an inverse Radon transform, depth and lateral positions can be resolved without lateral scanning.

[029] Each source light wavefront will also produce a fluorescence signal, Sw_f. To distinguish the interference signal Si a single wave-front signal S_Wf, the difference between the optical path lengths along paths 34, 64 and along paths 36, 40 is deliberately changed periodically, which causes the interference pattern within the sample 26 to move. Consequently, the amplitude of light from a stationary fluorophore within a sample is modulated. This amplitude modulated signal is used to form the HFT image. Provided that the period of the modulation is long compared to the fluorescence lifetime of the fluorophore, the fact that fluorescence is a stochastic process does not limit the resolution of HFT.

[030] In addition, unlike OCT, in HFT coherence only needs to be maintained along the paths into the sample. The light emitted from the sample represents the interference pattern and does not need to be coherent. Therefore, any fluorescent light, scattered or otherwise, contributes to the HFT image, which increases penetration depth compared to OCT where both the incident and reflected light must maintain coherence.

[031] Once the data has been collected, it is used to reconstruct a three-dimensional image of the sample. The image reconstruction algorithm decomposes the problem into two steps. First, a wave-length sweep is performed for each sample point, which yields the discrete Fourier transform (DFT) of the fluorophore density distribution over the set of hyperbolic shells that are defined by the illumination of geometry. Therefore, the first step is simply to apply the inverse DFT to obtain the density distribution in the spatial domain. The second step is then to apply the inverse Radon transform to the collection of all sample points to obtain a 3D image of the sample volume. This is the outline for reconstructing images where the two illumination points are relatively far apart, which is the case for the HFT configurations disclosed herein.

[032] For example, referring again to Figure ID, fluorescence data from a sample may be obtained and three-dimensional image of the sample may be reconstructed by obtaining data at multiple angles (α, β) of beams 64 and 40, respectively, according to the following steps:

1. Set 7N-n and γΝ-η + δ, where N is the maximum number of frequencies γ and n is a counter starting at 1.

2. Set mirror angles ocM_-m and βΜ-m, where M is the maximum number of mirror angles and m is a counter starting at 1.

3. Illuminate the sample with collimated y^._n from path 1 at angle 0CM-m, and collimated ^ηγκ-η + δ from path 2 at angle βΜ-m, thereby producing a hyperbolic interference pattern detected by the fluorophores within the sample that moves back and forth at the beat frequency δ, thereby causing the light emitted from the fluorophores to be modulated at the beat frequency δ. 4. Capture a two-dimensional image of the sample with an array-detector camera and store the image data as a function of the mirror angles (aM-_m,P -m), wavelength (γ_Ν._η) and detector position (XT), which represents a projection on the plane of the detector for mirror angles (a -m,PM-m) a d wavelength (γ _-η) of a one- wavelength-dimensional Fourier transform of the fluorophore density distribution in the three-dimensional sample over the set of hyperbolic shells that are defined by the illumination geometry.

5. Iterate n, select a new wavelength γ_Ν-_η and repeat steps 1 - 5 until n = N.

6. Iterate m, select new mirror angles (ocM-m^M-m) and repeat steps 1 - 7 until m = M.

Note: The resultant images IMN represent projections on the plane of the detector of a N- wavelength-dimensional discrete Fourier transform of the fluorophore density

distribution in the set of hyperbolic shells that are defined by the illumination geometry for M source angles.

7. Perform an inverse Fourier transform on all images ¾M to obtain the density distribution in the spatial domain.

8. Perform an inverse Radon transform to obtain a three dimensional image of the sample volume, as will be understood by persons skilled in the art.

[033] However, it is to be recognized that various approaches to reconstruction of the image of the fluorescence data may be used without departing from the novel principles disclosed herein.

A Single-Objective HFT System

[034] A schematic diagram of a preferred embodiment of a single objective HFT system 80 incorporating the principles of the invention is shown in Fig. 3. In this system, light from a tunable, long coherence length laser 82 is directed through an acousto-optical crystal modulator ("AOM") 84, which is used to achieve frequency shifting. The deflected, first order beam 86 is skewed with respect to the direction of propagation of the acoustic wave within the AOM crystal, shown by arrow 88, thus its frequency is altered with respect to the direction of propagation of the zero order beam 90 due to the Doppler effect. For example, if the AOM is operated at 70 Mhz, the frequency of the first order beam is shifted with respect to the zero-order beam by 70 Mhz. For a laser beam of 580 nm or 516.9 Thz, a 70 Mhz shift is normally insignificant.

However, in the present embodiment, this frequency shift; also means that the interference pattern within the sample volume changes 7 million times per second, and that the amplitude of the fluorescence will be modulated with this 7 Mhz frequency. Detecting modulation frequencies in the radio frequency ("RP") domain has a number of advantages. The most important of which is that heterodyning preserves phase information in the RF signal, so that the HFT signal carries more information than ordinary square wave detectors directly sensing the mixed light beams can provide.

[035] In this embodiment, the RF power into the AOM, provided by RF generator 92, is preferably adjusted so that the zero and first order beams are of equal intensity. The zero order beam is directed to a first beam expander 94, in this case for example by three mirrors 96, 98 and 100. The first order beam is directed to a second beam expander 102, in this case for example by two mirrors 104 and 106. Beam expander 94 illuminates aperture 108 and beam expander 102 illuminates aperture 110. The beams 112 and 114, that is, portions of expanded beams 90 and 86, that pass through the respective apertures 108 and 110 are then recombined by beam splitter cube 116. This beam splitter plays no role in the Mach-Zehnder interferometer because the beams 112 and 114 that propagate through apertures 108 and 110, respectively, enter the beam splitter cube 116 from different facets. The beam splitter only serves to combine the two beams in two different combined-beam branches 118 and 120.

[036] The beam outputs from the beam expanders 94 and 102 were shaped with two respective apertures, that is_? a circular aperture and an annular aperture, and combined with a beam splitter cube 116. A portion of beam 120 from the beam splitter 116 was directed by another beam splitter to the reference detector 134 which comprises a photomultiplier with a 1 μπι pinhole and a neutral density filter. However most of beam 120 was routed to a 800 mm telescope lens and focused on a CCD camera whose output was used to align the two combined wave-fronts in beam 120 so that they were parallel within a pointing error or less than 6 μ rad.

[037] In branch 118 the beams are combined so that they both can fill the back aperture of the same objective 122. The combined beams pass through a dichroic mirror 124 that reflect fluorescent light from the sample 126 to a signal detector 128 such as a photomultiplier tube ("PPT"). In branch 120 the combined beams are focused by lens 130 onto a pinhole 132 in front of a reference detector 134. Ideally, the reference detector is unnecessary. The output of the RF- generator could be used as a reference. However, commercially available AOMs often exhibit a large and very temperature dependent phase shift. Therefore, it is preferred to sense the actual beat signal between the two beams explicitly to avoid random phase drift from AOM 84.

[038] The objective lens 122 focuses the light to a spot within the sample 126. The same objective also collects the fluorescent emission from the sample, which is mounted on a precision actuated X/Y/Z stage 136. This light is directed by the dichroic mirror 124 through an emission filter 138 that blocks the laser light from the signal detector 128. The detector does not form an image in this case; rather, a beam from the infinity corrected objective reaches the detector substantially collimated. A signal 140 from signal detector 128 is processed with an RF lock-in amplifier 142 that yields a phase component 144 of the HFT signal and a magnitude component 146 of the HFT signal.

[039] A three-dimensional image of the sample may be reconstructed according to the following steps:

1. Set γι and yi + δ.

2. Illuminate the sample with γι from path 1 and ηγι + δ from path 2, thereby producing a hyperbolic interference illumination pattern detected by the fluorophores within the sample that moves back and forth at the beat frequency δ, thereby causing the light emitted from the fluorophores to be modulated at the beat frequency δ.

3. Capture light emission from the sample with a sensitive point-detector (photomultiplier) and store the this data as a function of position (XT), phase (Φ) and wavelength (γ), which represents the discrete one-wavelength-dimensional Fourier transform of the fluorophore density distribution in the three-dimensional sample over the set of hyperbolic shells that are defined by the illumination geometry.

4. Select a new wavelength γ₂ and repeat steps 1 - 3.

5. Repeat steps 1 - 4 until all emitted intensities for j through γ_η are captured and

corresponding data is stored, "n" being the maximum number of wavelengths used, which represents a projection on the plane of the detector of a n- wavelength-dimensional discrete Fourier transform of the fluorophore density distribution in the over the set of hyperbolic shells that are defined by the illumination geometry. 6. Perform an inverse Fourier transform to get the density distribution in the spatial domain.

[040] Alternatively, as suggested by Figure ID, two objectives could be used to illuminate the sample volume and, perhaps, a third objective could be used to collect the fluorescent emissions. While this could provide more flexibility, achieving stability would present a greater challenge.

Discussion of Simulated Results for Single Objective System

[041] In the single-objective lens system described above two light beams illuminating the sample may be produced by dividing the back aperture of the objective into two regions, each of which is illuminated by a different wavefront, thereby producing two distinct output beams that exit the front aperture of the objective and are focused to the same spot in the sample. Because the two output beams are distinct and have sufficient coherence length, they interfere in the sample. Because, as explained above, they have slightly different frequencies, which is equivalent to continuously changing their relative phase, they produce an HFT signal for the illuminated spot.

[042] One example of this approach is illustrated by Fig. 4, where the back aperture is divided into a concentric pattern 150 having a central circle 152 that receives one wavefront and a surrounding annulus 154 that receives the other wavefront. Both wavefronts are focused to the same spot 156 in the sample 26, but each has a different angular spectrum a and β, respectively. Consequently, they interfere with one another. In addition, because each beam has a different frequency, the detected amplitude of the two beams varies at a given spot at the lower beat frequency of the two beams which, preferably, is a radio frequency as explained above. This is manifested not only as a sinusiodally changing amplitude as a function of relative phase of the two beams at a given spot, but as a sinusoidally varying change in position of the location of maximum intensity as a function of relative phase, as shown by the instantaneous amplitude of the electromagnetic field near the focal point of the objective in interference patterns 158, 160, 162 and 164 in a (X-Z) plane including the optical axis of the objective. As the phase difference increases the focal point of the objective moves up, and vice versa. The white point illustrates the location of a fluorophore and the graph 166 shows the intensity of the fluorescent light emitted by that fluorophore as a function of time. The average intensity 170 of the fluorescent light corresponds to the signal that a conventional imaging system would produce. The amplitude of the modulation and its phase are the signals that the HFT system uses to form an image. The phase is also a function of position along the optical, Z-axis of the objective.

[043] In addition to the back aperture division configuration shown in Fig. 4, two other configurations are shown in Fig. 5, along with their resulting interference patterns the X-Z plane (A-Scan) and a (X-Y) plane perpendicular thereto (C-Scan) and their corresponding phase distributions. More specifically, Fig. 5 shows the concentric pattern 150 and corresponding A- Scan 172 and its phase distribution 174, and C-Scan 176 and its phase distribution 178; a double- D pattern 180 and corresponding A-Scan 182 and its phase distribution 184, and C-Scan 182 and its phase distribution 188; and a double-circle pattern 190 (wherein a portion 192 of the aperture is dark) and corresponding A-Scan 194 and its phase distribution 196, and C-Scan 198 and its phase distribution 200. The concentric configuration is asymmetric in the sense that the two beams arrive at the focal point with different angles relative to the optical axis, as opposed to the double-D and double-circle configurations, where both beams have the same shape and arrive at the focal point with the same angular distributions. The concentric configuration also differs from the double-D and double circle configurations in that the concentric configuration has an intrinsic ability to sense position along the Z-axis, while the double-D and double-circle configurations yield no Z-resolution in the Y-Z plane (B-Scan), that is, the plane including the optical axis of the objective that separates the two illuminated regions. On the other hand, the symmetric configurations have higher resolution in the X-Y plane. To utilize this advantage fully, the illumination pattern should be rotating so that each point is sampled with two or more configurations to achieve isotropic resolution. The concentric configuration yields a simpler system with better Z-resolution without relying on a Radon transform as explained below.

[044] These results were obtained by simulation through numerical solution of a Fresnel- Kirchoff diffraction model for a discretized 3D volume.

Example Test System and Results

[045] A system substantially as illustrated in Figure 3 and described herein was constructed, its HFT point spread function (PSF) was measured and HFT images were produced.

1. The Test System [046] The system was implemented with conventional free-space optics on a vibration isolated optical table. The tunable laser (corresponding to element 82 in Fig. 3) comprised a dye-laser that was pumped with an argon-ion laser. The dye-laser was modified for electronic tuning. It included a custom Yag-etalon with a free spectral range of 79.225267 Ghz. Stable operation was possible on 570 distinct lines, from 579.9 nm to 635.5 nm, each about 6 Ghz wide. They dye laser produced about 250 mW when pumped with 4 W. The output of the dye laser was fed through an electro-optical amplitude stabilization system. The beam was then directed through an AOM (84). The zero-order beam was reflected off two mirrors on a movable stage to the beam expander (94). The first-order beam was directed to the beam expander (102), which included a 6 μιη pinhole that acted as a spatial filter for the laser beam. The second order beam was directed at a beam position sensor for alignment purposes. The beam position sensor is also used to determine the dispersion of the AOM. Because the system swept the laser over a range of about 55 nm, the wavelength dependent AOM deflection angle could cause misalignment. Compensation for this was accomplished by changing the AOM operating frequency.

Compensation for dispersion was also accomplished by electronically changing the AOM frequency (about 67 to 73 Mhz). A delay adjustment stage was used to equalize the optical path- lengths. By sweeping the laser and recording the phase between the reference signal and the AOM drive, the optical path was equalized programrnatically to below 1/10 wavelength.

[047] The beam (118) passed through a dichroic mirror (124) and was focused onto the sample with an infinity corrected 25X, NA=0.65 objective microscope (122) mounted horizontally on a piezo-electric stage (136) that allowed rapid Z-scans over a 100 μηι range with a 0.7 nm resolution. The fluorescence signal detector (128) was a PMT protected from the excitation light with an interference filter (138). The signal from the PMT was amplified with a combined low- noise and an RF-lock-in amplifier (142).

2. The measured point spread function

[048] The point spread function (PSF) was measured by imaging 0.2 μπι microspheres with a voxel size of 0.33 μm/side and averaging over 22 isolated spheres that were manually selected. Example results are shown in Figure 7. Image 152 of Figure 7 is the PSF obtained by recording the overall PMT current at a wavelength of 587.3 nm. It is essentially equivalent to the PSF of an ordinary light microscope. Given a numerical aperture of 0.65, the expected Rayleigh resolution was 551 nm in the XY plane at the focal point. The resolution measured from the average PMT current is only about 2 μιη. This degradation by a factor of 4 is due to the fact that it is averaged over all possible phase shifts. Also, there was somewhat more power in the central zone than in the outer zone.

[049] Integrating the PSF over cylindrical shells around the focal point should yield a 1/r decrease of the signal per voxel due fact that the volume of a cylindrical shell with constant thickness increases proportional to the radius. The magnitude of the HFT signal in the current configuration, shown by image 152 decreases more rapidly and is proportional to r^—l-8 · This approaches the inverse square dependency shown by true confocal microscopy or more recently by two-photon excitation microscopy. It is expected that an even sharper PSF fall-off would be possible if the two illumination zones were separated by a dark ring.

[050] Image 154 in Figure 6 is the phase of the HFT signal, which shows the gradient along the X-axis. The total phase change of the usable portion of the PSF was about 2.5 rad. This was in line with the simulation, but it may be desirable to increase this range. For example, deliberately focusing the two beam expanders in opposite directions will have the effect of moving the two virtual emission points apart along the Z-axis while maintaining rotational symmetry.

Additional Disclosures

[051] Applicant hereby incorporates Appendix I entitled "Additional HFT Disclosure" as part of the specification of this application.

[052] Applicant hereby incorporates Appendix II, which is a copy of a United States Patent Application No. 13/298,066, entitled LOW NOISE PHOTO-PARAMETRIC SOLID STATE AMPLIFIER as part of the specification of this application.

[053] Applicant hereby incorporates Appendix III, entitled "Quad-Galvos-Synthesized Beam Rotation/Scanning" as part of the specification of this application. APPENDIX I

ADDITIONAL HFT DIBCLOSITCE

1 Introduction

Every once in a while, optical imaging technology is advanced by an idea that can be described succinctly in one sentence. Minsky's idea to illuminate only the sensing spot of a scanning imager by using the objective lens to project a point light source into the sample, gave rise to confocal microscopy [9, 8, 11]. More recently, Fujmoto invented optical coherence tomography (OCT), which uses an interferometer to discriminate coherently scattered light by its optical path-length [3, 6, 15, 2], Likewise, heterodyne fluorescence tomography (HFT), which is proposed here, relies on one concise idea: using organic fiuorophores as coherent wavefront detectors. Like confocal microscopy and OCT, the idea behind HFT is quite general and can be implemented in a number of different ways. The research presented in this proposal is specifically aimed at biological and medical applications where imaging the locations of fluorescently labeled molecules or cells is needed and where the operating depth of confocal microscopy is insufficient. The practical operating depth of confocal microscopy is about 100μ«?, while OCT can resolve structures up to about 20x deeper. However, OCT images are formed from back-scattered light that can only show morphology, while confocal microscopy can employ fluorescent labels to show the locations of specific molecules, HFT promises the best of both technologies: high resolution fluorescent imaging at penetration depths comparable to that of OCT.

OCT has been described as radar that uses infra-red light instead of microwaves [3], The distance from the instrument to the location of the structure within the sample that causes light to be reflected is measured by the optical path length induced delay of the reflected light. For OCT to form an image, the reflected light must maintain coherence back to the interferometer, thus the image formation mechanism is back-scatter from discontinuities in the refractive index of the sample (Fresnel reflection), which yields images of the sample morphology without any molecular specificity. HFT can be compared to radar that uses transponders, which are devices that receive the radar signal and then transmit a response on a different frequency [14]. In this analogy, the fluorescent organic dye molecule plays the role of the transponder, The fiuorophore is excited by the interrogating light at one wavelength and responds with a fluorescent emission at a different, lower frequency. However, this analogy is flawed by the fact that a radar transponder replies with a precisely defined delay, while the process of fluorescence involves an unpredictable delay (~-l-10ns) that is very long compared to the required temporal resolution to form a good image (~3-10fs). HFT overcomes this problem by using an intermediate frequency (IF) that has a period that is much longer than the temporal jitter of fl

A) Basic OCT B) ach-Zehnder OCT C) Rube Goldberg OCT D) HFT

Figure 1: Evolution of OCT to HFT

Figure 1 illustrates the basic principles behind OCT and HFT. The classic OCT setup (A) employs a Michelson interferometer where the light from a source (LS) with short coherence length is split (BS) into two paths. The first path is directed at the sample (S) while the second path is reflected off a reference mirror (RM), The reflected light from both paths is recombined in (BS) and directed at a detector (D). The detector will sense an interference signal only if the optical path lengths of the reference and sample arm are within the coherence length of the light source. Thus it is possible to obtain a range profile by moving the reference mirror. Panel B) of Figure 1 depicts a hypothetical OCT system that uses a Mach-Zehnder interferometer instead of the Michelson configuration. Again, the light is split into two separate paths that interfere only if their respective path-lengths are within the coherence length. The capabilities of this configuration do not differ significantly from the basic OCT system. However the fact that the incident and reflected light travel along different paths means that this configuration is not compatible with the confocal scanner that is normally used in an OCT system. Panel C) of Figure 1 uses the same Mach-Zehnder configuration, but it replaces the beam splitter (BS2) with a fluorescent screen (FLS). If the two paths of the interferometer are within the coherence length, then the two wave-fronts will create an interference pattern on the screen that can be observed with the detector (D). The gratuitous introduction of fluorescence does not change the operating principle: the interference could be observed either directly with a CCD camera, a photographic plate, etc. or indirectly by observing the fluorescence light. In either case, the observed signal is proportional to the square of the sum of the two incident electro-magnetic waves at the point of the FLS. Naturally, this Rube Goldberg contraption has no advantages over the basic OCT set-up, but it sets the stage for HFT, which is depicted in the last panel of Figure 1. Again, this is basically a Mach-Zehnder interferometer. However, the sample is now the detector. Or more precisely, the fluorophore within the sample volume will serve as a detector in this interferometer: the light from the source (LS) is split into two paths that are both directed at the sample via the mirrors RM1 and RM2. The fluorescent molecules within the sample volume are excited by the coherent sum of both wave-fronts and act as square-law detectors. The emitted light from the fluorescence is subsequently received by the external detector (D) which is blind to the excitation light. In order to distinguish the interference signal from fluorescence that is caused by just one wave- front, the optical path-lengths difference is deliberately changed in a periodic fashion, which in rum causes the interference pattern within the sample volume to move. Therefore the amplitude of the light from a stationary fluorophore within the sample is modulated. This amplitude variation is the signal that is used to form the HFT image. Provided that the period of the modulation is long compared to the fluorescence lifetime of the fluorophore, the fact that fluorescence is a stochastic process does not limit the resolution of HFT. It should also be noted that unlike OCT, coherence only needs to be maintained along the path into the sample. The light emitted from the sample does not need to maintain coherence. Therefore any fluorescent light, scattered or otherwise contributes to the HFT image, which increases penetration depth compared to OCT where both the incident and reflected light must maintain coherence.

The next section will describe the proof of concept system that was built and the results that were obtained so far. This system is the first implementation of HFT. These results are very recent and have not been published yet. Section 3 has a detailed description of the proposed research and development. It is followed by a discussion of the proposed new system, its application and capabilities. This technical description will conclude by describing the intellectual merits and the broader impact of this research.

2 Proof of Concept HFT System

Interferometers compare optical path lengths. This leads to a fun¬

Figure 2: OCT vs. HFT Sensing damental difference between OCT and HFT, namely that OCT can sense the round-trip optical path length, while HFT senses the optical path length difference. Consider the Mach-Zehnder OCT configuration from Figure 1: any scatterer S that is located on an elliptical shell whose two focal points are the points in BS 1/BS2 where the light is split/recombined will produce the same signal. In the case of the Michelson OCT configuration, the ellipsoid degenerates to a sphere with the center on the beam splitter. Thus OCT senses depth (Z) while lateral resolution (X Y) depends on a confocal scanner. In the case of HFT (Figure 1, D) all fluorophores that are located on hyperbolic shells that are defined by focal points on RM1 and RM2 will produce the same signal. In other words, any point within the sample volume that has the same distance difference from RM1 and RM2 will generate the same signal. This relation is illustrated in Figure 2, where the two points on the left indicate the focal points. In the case of OCT, one point is the emitter while the other is the detector, while in the case of HFT both points are the location of the emitters¹. Consequently, HFT has better resolution in the X/Y plane and cannot resolve Z along the line of symmetry, while OCT cannot resolve X/Y. Therefore while OCT can directly resolve Z, HFT requires multiple acquisition steps with different emitter pairs and an inverse Radon transform to resolve Z (and X/Y). It should be noted in this discussion that the amplitude or sensitivity of either system strongly depends on how the light is focused into the sample volume. Illuminating the sample with unfocused, spherical waves would be rather inefficient in either case.

As outlined in the previous paragraph, choosing an illumination configuration is a critical design decision for an HFT system. Figure 1 suggests the use of two objectives to illuminate the sample volume and perhaps a third objective to collect the fluorescent emissions. While such a set-up would provide the most flexibility to explore the HFT design space, it is also quite complex and fraught with stability problems. Therefore a single objective configuration was considered, where both illumination beams are projected into the sample through a single objective lens.

Figure 3 shows one single objective HFT

configuration. The light from a tunable, long

coherence length laser is directed through an

acousto-optical modulator (AOM). Normally,

AOMs are used to deflect laser beams, filter out particular wavelengths or modulate the

amplitude, but in this case, the AOM is used

as a frequency shifter. The deflected, first order beam is not perpendicular to the direction

of propagation of the acoustic wave within the

AOM crystal, thus its frequency changes due

to the Doppler effect. If the AOM is oper

ated at 70Mhz, the frequency of the first or¬

Figure 3: Single Objective HFT

der beam is shifted with respect to the 0-order

beam by 70Mhz. For a laser beam of 580nm or 516.9ΊΉζ, a 70Mhz shift is normally insignificant. However, this frequency shift also means that the interference pattern within the sample volume changes 70M times per second, and that the amplitude of the fluorescence will be modulated with this frequency. Detecting modulation frequencies in the RF domain has a number of advantages. The most important of which is that heterodyning preserves phase information, thus the HFT signal carries more information than ordinary light detectors can provide.

The RF power into the AOM is adjusted so that the zero and first order beams are of equal intensity, These beams are then directed to two beam expander BEl and BE2 that illuminate the apertures Al and A2. The expanded beams are then recombined with the beam-splitter (BS). This beam splitter plays no role in the Mach-Zehnder interferometer because the apertures Al and A2 do not overlap, thus each part of the beamsplitter cube is illuminated by at most one branch. It serves only to combine the beams so that both can fill the back aperture of the same objective (Obj). The combined beams pass through a dichroic mirror (DCM) that will reflect the fluorescent light from the sample to the signal detector (SD). The beam-splitter produces two combined beams. The second beam is focused with a lens onto a pin-hole in front of the reference

'The location of the detector is irrelevant for HFT. In fact, there can be multiple detectors or area detectors in order to capture more light. detector (RD). Ideally, the reference detector is unnecessary. The output of the RF-generator could be used as a reference. However, the commercially available AOMs exhibit a large and very temperature dependent phase shift. Therefore it is better to sense the actual beat signal between the two beams explicitly to avoid the random AOM phase drift.

° 90° 180° 270°

Figure 4; Single objective lens HFT

The objective lens (Obj) focuses the light onto a spot within the sample (S). The same objective also collects the fluorescent emission from the sample. This light is directed by the dichroic mirror (DCM) through an emission filter (EF) that blocks the laser light from the signal detector (SD). The detector does not form an image in this case, rather all light from the infinity corrected objective reaches the detector. The signal from SD is processed with an RF lock-in amplifier which yields both phase and magnitude of the HFT signal. For the proof of concept system, the sample is mounted on an actuated precision X/Y/Z stage.

2.1 Simulation Results

The HFT system outlined above was motivated by simulations that showed that dividing the back-aperture of an objective lens into two regions, each of which is illuminated with one wave-front, yield a practical HFT signal. Figure 4 illustrates this idea: in this case, the back aperture of the objective lens is divided into two concentric zones, a central circle surrounded by a ring. The two planar wave-fronts filling each zone have slightly different frequencies, which is equivalent to continuously changing their relative phase. Figure 4 shows the instantaneous magnitude of the EM-field near the focal point of an objective lens. These results were obtained through numerical solution of the Fresnel-Kirchoff diffraction for a discretized 3D volume, The first image simply shows the point spread function of the objective because a phase difference of 0 between the two planar waves entering the back aperture of the objective is equivalent to just one uniform planar wave, As the phase difference increases, the focal point of the objective appears to move up. The white point illustrates the location of one fiuorophore and the graph below shows the intensity at this point as a function of time. The average intensity corresponds to the signal that a conventional imaging system would produce. The amplitude of the modulation and its phase are the signals that the HFT system uses to form an image. It should be noted that the phase is a function of the position along the Z-axis. A configuration that produces a large change in the phase when a point is moved through the sample volume can be expected to yield better resolution.

Figure 5: Single Objective HFT Simulation Results

Figure 5 shows the simulated HFT point spread function for three configurations, concentric rings, two half circles and two circular sub-apertures. The top row of pictures show the color coded magnitude of the HFT signal in the XZ and XY planes (A and C-scan). The second row shows the corresponding phase, where the angular range of 0-360 degrees is mapped to a color ring, where black represents 0, blue 90, white 180 and red 270 degrees. The first configuration is asymmetric in the sense that the two beams arrive at the focal point with different angles relative to the optical axis, as opposed to the later two configurations where both beams have the same shape and arrive at the focal point with the same angular distribution. The interesting distinction is that the first configuration has an intrinsic ability to sense position along the Z-axis, while the later configurations yield no Z-resolution in the YZ-plane (B-scan). On the other hand, the symmetric configurations have higher resolution in the X/Y plane. To fully utilize this advantage, the illumination pattern should be rotating so that each point is sampled with two or more configurations to achieve isotropic resolution. The first configuration is interesting because it yields a simpler system with better Z-resolution without relying on the inverse Radon transform.

2.2 Optical Setup

The proof-of concept system (Figure 6) was implemented with conventional free-space optics on a vibration isolated optical table. The optical layout mostly follows the schematic from Figure 3. The light source is a tunable dye-laser that is pumped with a Coherent IONOVA-100 argon-ion laser. The dye-laser is based on the Spectra-Physics SP375B folded cavity laser, which was modified for electronic tuning. It also has a custom Yag-etalon with a free spectral range of 79.225267 Ghz. The line-width is monitored with a Candela LS-1 laser spectrometer and the wavelength is measured with an Advantest Q8326 wavelength meter, Using Rhodamine 6G, stable operation is possible on 570 distinct lines, from 579,9nm to 635.5nm, each about 6Ghz wide. A fraction of the output beam from the dye laser is monitored with a Coherent beam-profiler

Figure 6: HFT Proof of concept implementation

(P). The dye laser was aligned for maximal stability, not for maximal power, and produces about 250mW when pumped with 4W.

The output of the dye laser is fed through an electro-optical amplitude stabilization system (Canop- tics LASS-II Noise-Eater, NE). This system had to be modified for broadband operation because it uses a wavelength-depended bias voltage. The circuit determining this voltage was very slow and caused large fluctuations when the wavelength was changed. The modification consisted of supplying an external bias voltage that is controlled from the computer that also controls the rest of the HFT system and which collects the image data (a high end white-box PC running Linux).

The beam is then directed though a NEOS Te02 AOM (AOM), which is mounted in a machined aluminum box which also includes the RF-power amplifier and a frequency doubler. Hermetic sealing is necessary because the AOM requires about 1 W of RF-power. The signal detector is essentially a very sensitive radio-receiver that operates on the same frequency. Therefore even minute leakage from the AOM driver could cause interference. After the AOM is a variable attenuator (AT). The first order beam is directed to the beam expander BE1, which also includes a 6μ η pinhole that acts as a spatial filter for the laser beam. The second order beam is directed at a beam position sensor (BPS) for alignment purposes. The BPS is also used to determine the dispersion of the AOM. Because the HFT system sweeps the laser over a range of about 55nm, the wavelength dependent AOM deflection angle would cause miss-alignment. This is compensated by changing the AOM operating frequency accordingly. A dispersion compensator was computed which would allow constant intermediate frequency (IF) operation over the whole wavelength range at the expense of two custom prisms, but electronically changing the AOM frequency (about 67 to 73 Mhz) is the simpler and cheaper solution to this problem. The zero-order beam is reflected off two mirrors on a movable stage (DA) to the beam expander BE1. The delay adjustment stage is used to equalize the optical path-lengths. By sweeping the laser and recording the phase between the reference signal and the AOM drive, the optical path is equalized programmatically to below 1/10 wavelength.

The beam outputs from the beam expanders are shaped with two apertures and combined with a beam splitter cube on an electronically adjustable stage (BSS). The output towards the bottom of the picture is directed to the reference detector (RD) , which is a Hamamatsu photomultiplier with a Ιμπι pinhole and a neutral density filter. However most of the beam is routed to a 800mm telescope lens (TL) which is focused on the CCD camera (C). This is an alignment aid that is used to align the two wave-fronts so that they are parallel, which is achieved by adjusting the BSS. This was the most difficult alignment step for this set-up. With the addition of this telescope, alignment became very easy and precise. It takes about 30 seconds to achieve a residual wavefront pointing error of less than >μταά. This beam path also allows easy insertion of a shear-plate collimation tester to focus the beam expanders. MT Current HFT Magnitude HFT Phase

The main beam passes horizontally to the left through the dichroic mirror (Semrock FF670-SDi01) and is focused onto the sample with an infinity corrected microscope objective (Reichert 25X, NA=0.65). The objective is mounted horizontally in a Physics-Instruments piezo-stage that allows rapid Z-scans over a ΙΟΟμηι range with 0.7nm resolution. The fluorescence is detected with a Hamamatsu H6780-01 pho- tomultiplier rube (PMT), which is protected from the excitation light with an interference filter (Semrock LPD01-633RU-25). The signal from the PMT is amplified with a custom, low-noise amplifier (LNA) and send to a Stanford Research Systems SR844 RF-lock-in amplifier.

The sample is mounted on a Newport XYZ stage that uses 3 Physics Instruments M222-20 motorized micrometers. This stage has a resolution of about 0.1 μτη, which is sufficient for the proof of concept. However, it turned out that this prototype system has surprisingly high resolution. Thus it was tempting to insert a 100X oil-immersion, high NA objective to see if this result also is true for a high end objective, which yields a resolution that could exceed conventional light microscopes. Unfortunately, the stage resolution is currently insufficient for this experiment.

The left picture in Figure 6 shows the sample holder, PMT and BSS. The central obstruction to form the ring zone aperture stems from an Avery counting dot an a microscope slide, which limits the choice of inner beam diameters and is one aspect of this set-up in need of refinement.

23 Measured Point Spread Function

The point spread function (PSF) was measured by imaging 0.2μιη micro-spheres (Invitrogen TetraSpeck T14792) with a voxel size of

and averaging over 22 isolated spheres that were manually selected. The right image of Figure 7 is the PSF obtained by recording the overall PMT current at a wavelength of 587.3nm. It is essentially equivalent to the PSF of an ordinary light microscope. Given a numerical aperture of 0.65, the expected Rayleigh resolution is 551nm in the XY plane at the focal point. The resolution measured from the average PMT current is only about 2μιη. This degradation by a factor of 4 is due to the fact that it is averaged over all possible phase shifts. Also, there was somewhat more power in the central zone than in the outer zone, which also negatively impacts resolution. However, the magnitude of the HFT signal shows a resolution of about 340nm, which exceeds the expected resolution. This result was surprising, because resolution is not the main focus of this research, Deeper penetration and improved optical sectioning is the goal, However, this result is also right at the limit of the resolution of the current stage and has to be confirmed with a better scanning system.

Integrating the PSF over cylindrical shells around the focal point should yield a 1/r decrease of the signal per voxel due fact that the volume of a cylindrical shell with constant thickness increases proportional to the radius, The magnitude of the HFT signal in the current configuration decreases more rapidly and is proportional to r^{~ LS} . This approaches the inverse square dependency shown by true confocal microscopy or more recently by two-photon excitation microscopy, It is expected that an even sharper PSF fall-off is possible if the two illumination zones are separated by a dark ring, which is not practical with the current setup.

The right image in Figure 7 is the phase of the HFT signal, which shows the expected (See Figure 5) gradient along the Z-axis. The total phase change of the usable portion of the PSF is about 2.5rad. This is in line with the simulation, but it is desirable to increase this range. For example, deliberately defocusing the two beam expanders in opposite directions will have the effect of moving the two virtual emission points apart along the Z-axis while maintaining rotational symmetry.

2.4 Image Reconstruction Algorithm

The most direct image reconstruction algorithm decomposes the problem into two steps. First, a wavelength sweep is performed for each sample point, which yields the discrete Fourier transform (DFT) of the fluorophore density distribution over the set of hyperbolic shells that are defined by the illumination geometry. Therefore the first step is simply to apply the inverse DFT, to get the density distribution in the spacial domain. The second step is then to apply the inverse Radon transform to the collection of all sample points to get a 3D image of the sample volume. This is the outline for reconstructing images where the two illumination points are relatively far apart, which is the case for the HFT configurations proposed below.

However for the current proof of concept system, this strategy is not practical because the single objective lens configuration means that the two virtual emission points are very close to each other, which in turn means that there is a much smaller wavelength dependency of the phase map. In practice, this means that most of the signal is concentrated in the first or second bin of the inverse DFT. Compounding this problem is the fact that the phase map is rather complex due to the diffraction effects which dominate over the geometrical distribution. Thus the actual reconstruction algorithm for the prototype omits the inverse DFT step and folds it into the Radon transform. Using fewer wavelengths (5 to 10 instead of 570), the increase of the size of the system matrix is still within the capability of contemporary PC hardware. Currently, a quad-processor PC with 32Gbyte of memory running Linux (FC-7) is capable of reconstructing a 300 by 300 by 300 voxel image in about 30minutes. The computational requirements are no real disadvantage for HFT because of the rapid advance of PC hardware. In particular the recent announcement from NVIDIA [10] that their next generation graphics processing unit (GPU) will support 64bit floating point arithmetic will make it likely that HFT image reconstruction can be erformed in real time using the GPU.

2.5 Preliminary Results

The proof of concept system became operational in March 2008 and has since undergone a number of significant refinements.

The control and data analysis software, totaling

some 40,000 lines of C and C++ code is still far

from complete, but is functional enough to align

and calibrate the system and to collect data. While

the the full image reconstruction software is still

in the debugging phase, images where obtained because the single objective configuration has a fairly

localized PSF so that the raw data resembles an im

age. The raw images show however a number of characteristic artifacts, for example speckles due to the coherent nature of HFT. 14 052589

Figure 8 is an example of a raw HFT image. Each panel is a 300x300 pixel slice of an 100x100 micrometer area. The top row is a C-scan (X Y-plane) of structures about ΊΟμπι below the surface of a plant leaf taken from our office decoration. Leaves make nice test samples because they have plenty of natural auto- fluorescence and because their cuticle and upper epidermis form a diffuse scattering layer which normally impedes microscopy. The test samples were unmodified leaves embedded in water and covered with a normal 0.17mm cover slip, Because the image acquisition time is rather long due to the slow stage mechanism, bleaching is severe, which can be seen in the image formed by the average PMT current (left panel). The scan proceeds from the top to the bottom and the first row is much brighter than the

rest. The lower image set is an A-scan (X/Z plane). About 2/3 from the top is a bright line, which was caused by a glitch in the laser amplitude stabilization system that briefly increased the laser power. This is interesting because the impact was much less notable in the HFT magnitude image (center column) and had practically no effect on the phase image (right column). Another interesting aspect of this image is that it was obtained with slightly missaligned beams. This means that the focal points of the wave entering the objective through the center circle and the focal point for the ring wave did not line up on the optical axis. This case had been simulated and produced the expected asymmetry of the HFT PSF. But it also shows the increased spatial resolution in the corresponding direction in the X/Y plane. This effect was discussed in section 2.1.

Figure 9 shows the same sample imaged with a Leica scanning confocal microscope. However it was not

possible to use the same objective lens, so this is not a

direct comparison. HFT has much higher spatial resolution at the depth of 70 μηι and beyond. However the true

sectioning abilities of HFT will not become obvious until

the image reconstruction software is fully operational.

Figure 10 is one slice of a more recent 300³ oxel scan

covering 100³μ?/ί of a fixated plant stem cross-section

without misalignment. It shows detail consistent with the

resolution of the PSF. It also shows speckle artifact because this is also a raw data-cube. Furthermore, no use

has yet been made of the recorded phase information yet.

2£ Lessons Learned

The first and most important result from the proof of con

cept system is that the HFT image forming mechanism

is indeed practical, Even with the currently incomplete Figure 10: Plant Stem HFT Image Slice image reconstruction software, the images show significantly improved penetration and optical sectioning compared to state of the art confocal microscopy. However, there are several issues that must be addressed before HFT becomes a viable and compelling imaging mode.

The image acquisition via stage scanning is too slow and must be replaced with a faster scanner^, Also, this scanner should have higher resolution so that possible improvements in the optical resolution beyond the Rayleigh criterion could be demonstrated unambiguously. The free-space optics should be replaced with a fiber-optic implementation. One of the stability issues stems from the fact that the longitudinal modes of the dye-laser also cause some spatial divergence, so that the mode mixture in the two beam-expanders can differ unpredictably. Coupling the laser into a single mode fiber before the AOM would clean up the beam.

The laser should be replaced with a ring-laser that has no longitudinal modes. There are several other desirable refinements of the laser, including faster wavelength switching times and temperature stabilization of the etalon.

Currently, the system operates in the yellow-orange region. It is desirable to move the operating wavelength to the near IR region. While this limits the choice of fluorophores (Alexa-680, Cy-7), it also greatly increases penetration. Furthermore, a suitable CW Ti-sapphire laser is more stable and does not require a noisy dye circulator.

The zone geometry should be controllable to optimize the HFT signal. It also should allow a dark zone between the zones and other patterns besides concentric rings.

The detector sensitivity, linearity and dynamic range should be improved. The current PMT is not optimal for operation in the red and near IR region.

3 The Proposed HFT System

The goal of this proposal is to build a practical and versatile HFT scanner that will be used and evaluated in ongoing bio-medical research at the Cedars-Sinai medical center. This device will be based on the experience gained from the proof-of concept HFT system described above. The current system is large, slow and requires a great deal of care to be used. The proposed system will be much smaller and can be deployed in a bio-medical laboratory to solve real problems. For example, with a scan depth of over 1 mm it will be possible to track cells in small organisms and embryos. The primary motivation for this work is the development of molecular imaging technology that is compatible with minimally invasive procedures. In particular to enable in-vivo, real-time, optical pathology. If it were possible to determine the health of tissue during surgery without the need of extracting biopsy samples and analyzing them in a pathology laboratory, cancer removal surgery could be greatly improved. This application requires a system that is compatible with a surgical microscope or an endoscope. It will be shown in section 3.5 that an Endoscopic HFT system is practical. This proposal seeks funding to build such an instrument and to demonstrate its utility, namely to increase the penetration depth of optical molecular imaging by about one order of magnitude over confocal microscopy.

3.1 Optica! layout

The proposed system will consist of two parts: 1. the laser and AOM subsystem and 2. the scan head. The AOM subsystem will be connected to a laser with a single mode, polarization maintaining, wide-band fiber (photonic crystal). Besides allowing easy switching of lasers, this use of fiber optics also mitigates the beam-pointing and mode-structure problems. The AOM subsystem will take care of amplitude stabilization, programmable attenuation, blanking, optical path-length equalization and frequency shifting, The optical output of the AOM subsystem is connected to a pair of matched fibers, which deliver the laser light to the scan-head,

The scan-head is a compact unit that can be attached to various stages and imaging optics. This ranges from dedicated objective lenses to the use of existing optical platforms, in particular surgical microscopes, stereo microscopes and the telecentric optics of a locally developed black-box for live animal investigations. The scan head includes the two beam expanders, the apertures, the beam combiner (aperture wheel), the detector and dichroic mirror, and the reference detector. The beam-splitter cube that was used in the proof of concept system is sub-optimal, because it adds two planar optical surfaces into the beam path. Even with a good anti-reflective coating, it caused extra interference and ghosting. Thus the new HFT system will replace this optical element with an aperture wheel which intersects the beam path diagonally. This wheel also has 26 patterned mirror zones that form the aperture and that will replace the Avery dot.

There will be two additional components that are not present in the proof of concept system: a galvo- scanner and a beam rotating prism. The galvo scanner replaces the stage scanning mechanism. The beam- rotating prism serves two functions. The first is to allow the use of apertures like the second and third of Figure 5. The second purpose is to allow rotation of the plane of polarization. It is also planned to use a detector pair that can sense the polarization of the fluorescence. By allowing the rotation of the excitation polarization, it is possible to sense the organization of certain biological structures, for example muscle fibers,

Frequency-agile ring laser

HFT depends on a CW laser that can rapidly switch wavelengths and that has a long coherence lengths . Some swept frequency lasers have been developed for OCT, for example from Thorlabs. But these lasers operate too far in the IR region to excite fluorescence and have too low coherence length for HFT. Most commercially available lasers that are tunable over a wide range and that have long coherence length rely on mechanically actuated wavelength selectors, that are intrinsically too slow for HFT.

However, it was experimentally verified that it is possible to replace the birefringent plate of a Lyot

Pump Inp, M1 M2 filter in a dye-laser cavity with a Pockels cell. A

FastPulse KD*P Pockels cell was used to rapidly Dye Jet ,< oc tune a SP375B dye laser. Unfortunately, KD*P is a bad material for this purpose because it will be

M3 PC1 PC2 damaged by prolonged exposure to DC-fields [4].

{RTP) (RTP) Thus a pair of custom RTP crystals was acquired

Figure 11: EO Tunable Laser that overcome this problem. Figure 11 shows this configuration. The custom crystals have been polished so that the entrance and exit faces admit the laser beam at Brewster's angle to minimize cavity loss and to enhance the selectivity of the Lyot filter.

It was considered to add this filter to a commercial ring- laser to overcome the longitudinal mode problem, but the

most suitable candidate , the new Spectra Physics Matisse laser,

would not be economical because it was designed for a much

lower line-width than that needed for HFT. Therefore a ring

laser was designed that is optimized for HFT. Figure 12 shows

the mechanical layout of this laser that uses mostly off-the

shelf components. The cavity was initially simulated with the

ABCD formalism [1 , 13 , 5] , but dye lasers use very fast, spherical mirrors and their aberrations need more detailed attention.

Adopting an idea from nuclear accelerators (alternating gradient focusing), it was found that by arranging the deflection Figure 12: FA Laser Cavity planes of the two spherical mirrors to be perpendicular to each

other, a much improved beam-profile was obtained. Unfortunately, this meant that the cavity beam path is no longer planar, which made for the awkwardly shaped bases (blue).

Figure 13: Opto-Parametric Amplifier

3.3 Opto-Parametric detection

Like most optical scanning platforms, the proof of concept system uses photomultiplier tubes (PMTs) as detectors. PMTs are attractive, because their built-in gain of up to 60db is nearly noiseless. Unfortunately, this gain comes at the expense of limited linearity, dynamic range and quantum-efficiency in the IR range. Solid state detectors have vastly more dynamic range, which is important for HFT because the detector sees a lot of fluorescence that stems from scattered light that does not contribute to the HFT image. Photodiodes also have higher quantum efficiency and nicely cover the near IR range. However they have no built-in gain and require amplification, which generates far more noise than the electron multiplication process in an PMT. Fortunately, an HFT detector only needs to be sensitive for signals within a narrow band around its intermediate frequency. Thus RF amplification techniques can be applied, which yield much less noise than broadband trans-impedance amplifiers for photodiodes [16]. Initially, the idea was to integrate the junction capacitance of the photo-diode into an impedance matching network connected to a low noise RF amplification stage. This approach was successful, but an even better solution is an opto-parametric amplifier (OPA). OPAs were originally developed by the US -Navy for optical communication with submersed submarines and patented in the early 1970s [7, 12].

Figure 13 shows the schematic and implementation of a 40MHz OPA. The key point is that the junction capacitance of a photo-diode depends on the reverse bias voltage. This means that the photo-diode can be used to periodically alter the resonant frequency of an LC network, which can act as a negative resistance that offsets the losses of the output resonator. The main property of an OPA is that it uses only reactances, which do not generate noise. This circuit was evaluated and compared to the performance of a PMT. It achieved a gain of over 60db. The gain of an OPA is bandwidth dependent, higher gain comes at the expense of reduced bandwidth. Thus at the bandwidth needed for HFT, an OPA provides about 25db of gain, which is more than sufficient because the noise figure of an RF amplifier is mostly determined by the first amplification stage. With a modest amount of cooling (-70C), the circuit in Figure 13 outperforms a PMT by nearly a factor of 10 in signal to noise ratio. It is also vastly superior with respect to sensitivity in the IR, linearity, and lack of short-term gain fluctuations.

3.4 Scanning without a scan-lens

Most scanning systems use a pair of galvanometers to facilitate deflection in the X and Y directions. Unfortunately, simple geometry can prove that it is impossible to build a scanner with just two galvos that can reflect a stationary laser beam through the center point of the back apertures of the imaging optics. Commercial systems typically overcome this problem by designing a scan-lens that takes the actual pivot point of the scanner into account. The scan-lens in the Leica confocal microscope is rumored to have consumed $1M in R&D. Regardless of the truth of this rumor, developing a custom scan lens is beyond the scope of this project. It is possible to avoid this problem with a set of relay lenses that projects a real image of the scan beam into the center of the galvo mirror. However this assumes that the axis of rotation lies in the surface of the mirror - which it doesn't - and that the mirror is near perfect, because its surface is being imaged as a byproduct. Another solution is to add a third galvo (top configuration in

Figure 14). Now that the galvo axes are no longer orthogonal, the

movements of all three mirrors must be tightly coordinated. This

approach became only feasible this year when Cannon introduced

a digital galvo, the G 15. This device uses a high resolution optical

encoder on the galvo axis and achieves a resolution of \&2μταά.

Furthermore, unlike conventional galvos that use an analog position sensor, this galvo senses absolute position with practically no

drift. Unfortunately, the three-galvo scanner requires the galvos to

be mounted precisely at very odd angles. Thus it is easier to use a

four-galvo configuration where all galvos are mounted in perpendicular directions. This has the additional benefit that the pivot

point is programmable so that this scanner can be easily adapted

to accomodate different imaging platforms.

3.5 Endoscopic HFT imaging system

So far, the discussion was primarily focused on one HFT configuration that uses an imaging objective. However, HFT is a Objective more general 3D sensing methodology that can be adapted to

Figure 14: Galvo Configurations non-traditional applications. Figure 15 shows the proximal end

of an HFT micro-endoscope. Using two galvos, the two light sources of the HFT system illuminate a pair of fibers of an image-preserving fiber bundle. Such imaging fiber bundles typically have 15000 to 30000 individual fibers and an outer diameter of 1 mm or less. For this HFT system, the fiber bundle must consist of single mode fibers. While these are available, bundles of polarization maintaining, single mode fibers are not. Thus one of the branches of this system needs a polarization controller or scrambler.

The distal end of this HFT micro-endoscope is shown in figure 16. It consists simply of a grin-lens that is fused to the fiber. Unlike ordinary endoscopes where the objective lens is supposed to form an image on the face of the fiber bundle, this system does not form an image, rather each fiber is intended to form a certain wavefront just ahead of the tip. Sim

ulations have shown that it is quite easy to configure the tip so that a cylindrical volume Figure 15: Endoscopic HFT Scanner of about 1 mm in diameter and 1 to 2 mm in length is illuminated. Image acquisition is accomplished by cycling through a large set of fiber pairs and performing one wavelength sweep for each pair. The fluorescent light from the sample volume is collected through all fibers simultaneously to maximize sensitivity. The 3D image is then computed using the inverse DFT followed by inverse Radon transform approach.

Unlike current confocal micro-endoscopes like

the CellVisio from Mauna Kea that scan only one

fixed plane, the HFT endoscope can sense a complete 3D volume. It is also expected that this system

will have a penetration depth on the order of 1 to 2

mm for biological tissues. Furthermore, the distal Figure 16: HFT Endoscope Tip end of an HFT endoscope is mucn simpler that that of other endoscopes, so t¾s it could be smaller, like the tip of a needle. Because it consists purely of glass, it is also easier to sterilⁱze.

4 Capabilities md Applications

The proof of concept system has shown the feasibility of HFT. We are refining HFT to a practical instrument and to show its utility in real bio-medical applications. The first device to be developed is a versatile and compact HFT scan-head that can be attached to existing microscopes. It will also be used in conjunction with an objective lens as a stand-alone system. The overarching aim of this group is to develop new technology for bio-medical applications. One demonstration application for HFT is noninvasive, real-time pathology during surgical procedures, which require molecular specificity, deep optical penetration, and high resolution. This application also motivates the proposed endoscopic implementation of HFT. Experience with Mauna Kea's CellVizio system has shown the utility, including clinical, of micro-endoscopy. With HFT it will be possible to increase the sample volume and capture full 3D structures instead of only thin 2D slices. It should be noted that a CellVizio-style system is limited by the number of fibers in the bundle to only about 3 OK pixels. The endoscopic HFT system can use the very same bundle to acquire (3 OK)² projections, each spatially resolved with a frequency sweep. That is equivalent to sensing over 1 billion voxels, which is a vast increase in resolution.

5 Intellectual Merits

HFT is a new imaging modality that extends the capabilities of confocal microscopy to penetration depths comparable to OCT. Increasing the ability to image molecules via fluorescence about 10 times deeper into biological tissues is clearly a significant advance of the state-of-the-art in molecular imaging. The viability of the principle behind HFT has been demonstrated. We seek to develop HFT to the point where its capabilities can be demonstrated in real, bio-medical research projects, and eventually clinical settings. HFT stands at the beginning of its development cycle and it is very likely that during the course of this research a number of significant refinements will be discovered. For example it was surprising to find evidence that HFT can potentially improve optical resolution beyond the ayleigh criterion. This observation begs to be verified and - if confirmed - exploited.

6 Broader Impact

The most direct impact of developing a more capable instrument such as HFT is that it enables research that is currently not practical or very difficult, for example m-vtvo tracking of stem cells. A successfully developed HFT system also has direct medical applications. Cancer margin determination during surgery is one such example. In fact the request of a neurosurgeon who treats brain-tumors in infants was one motivation for allocating precious research resources for the construction of the proof of concept HFT system, which has received no external funding to date. The concrete problem in this case is to determine the structure of the brain tissue in front of a micro-endoscope, which is opaque to conventional optics.

Finally, the broadest impact for HFT is eventual commercialization. Our group has excellent relations with leading microscopy vendors. In fact the opto-parametric solid-state detector that was developed for this project received interest for use in a scanning confocal microscope. This technology transfer could serve as a pathfinder for larger collaborations. The endoscopic version of HFT, with its clear performance advantages, should enable a significant clinical impact. 7 References

[I] G. E. Stedman B. E. Currie and R. W. Dunn. Laser stability and beam steering in a non-regular polygonal cavity. Applied Optics, 41:1689-1697, 2002.

[2] A.M. Rollins, S. Yazdanfar, J.K. Barton, J.A. Izatt, Real-time in vivo color Doppler optical coherence tomography, Journal of Biomedical Optics, 7:123-129, 2002.

[3] James G. Fujimoto. Pioneering new applications for OCT research. RLE Currents, 11(2), 1999.

[4] R. Goldstein. Electro-optical devices in review. Laser and Applications, April 1986.

[5] L. Liang B. Zhang F. Wang J. Yuan, X. Long and H. Zhao. Nonplanar ring resonator modes: generalized gaussian beams. Applied Optics, 46:2980-2989, 2007.

[6] D.Huang, EA.Swanson, C.P.Lin, J.S.Schuman, W.G.Stinson, W.Chang, M.R.Hee, TJFlotte, K.Gregory, C.APuliafito, J.G.Fujimoto. Optical coherence tomograpgy. Science, 254:1178-1181 , November 1991.

[7] W. E. Freitag, M. K. Giles. Photoparametric amplifying upconverter. US Patent number 3,937,979, 1976.

[8] insk . Memoir on inventing the confocal scanning microscope. SPIE MILESTONE SERIES MS,

131 :7-17, 1996.

[9] M. Minsky. U.S. patent number 3013467, microscopy aparatus. US Patent, 1957.

[10] NVIDIA. Nvidia glOO: Teraflops visual computing. In Hot Chips Conference, Stanford, 2008.

[I I] James B. Pawley. Handbook of Biological Confocal Microscopy. Plenum, 1995.

[12] D. E. Sawyer. A study on p-n junction photodetectors utilizing internal parametric amplification.

Defense Technical Information Center, Accession Number AD0610824, 1964.

[13] A.E. Siegman. Laser beams and resonators: Beyond the 1960s. Selected Topics in Quantum Electronics,

IEEE Journal of, 2000.

[14] M. Skolnik. Radar Handbook. McGraw-Hill, 2nd edition, 1990.

[15] Alex Tumlinson. Simultaneous optical coherence tomography and fluorescent imaging. Web site.

[16] M. Uenohara. Low noise amplification. Handbuch der Physik, 23, 1962.

APPENDIX II

LOW NOISE PHOTO-PARAMETRIC SOLED STATE AMPLIFIER

BACKGROUND

Field

[0001] The present disclosure relates to optical amplification, and particularly relates to a photo-parametric amplifier that uses the properties of solid state detectors for very low noise amplification of weak, pulsed, high frequency optical signals.

DescriptSoffi of Related Art

[0002] Many biomedical instruments require the detection of very faint optical signals. For example the fluorescence of a single dye molecule that is coupled to an antibody may yield information about where a particular protein is located within a cell, but it produces very few photons/sec even with strong illumination. Many instruments detect such weak light sources with photomultiplier tubes (PMTs), where a photo-cathode converts a photon into a free electron, which is then accelerated by an electrical field to a dynode. Typical PMTs use 10 dynodes and provide a current amplification by a factor of about one million.

[0003] The internal gain is the significant advantage for PMTs over solid state photo detectors which have no built-in gain mechanism and which have to rely on external electronics to amplify the photo current to usable levels. PMT optical amplifiers outperform those based on photo diodes (solid state photo detectors) in terms of overall sensitivity and signal to noise ratio, even though photodiodes are actually much better at sensing light. The quantum efficiency (i.e., the probability for one photon to generate one electron) of a photodiode often exceeds 80% while it is rare that a PMT has a quantum efficiency that approaches 30%.

[0004] Photo diodes are extremely linear devices, e.g., the current output is strictly proportional to the light input for over 12 decades while a PMT barely maintains linearity over 3 decades. Photodiodes are very rugged devices that are not harmed by exposure to high light levels, while PMTs are fragile and easily destroyed by exposure to room light levels while powered on. Photodiodes are available that operate well with IR light, while PMTs can barely detect light in the near IR spectrum. Photons with wavelength in excess of 1 micrometer do not have enough energy to free an electron, thus there are no practical PMTs that can cover the 1 - 2 micrometer wavelength range, while solid state detectors exist that can operate up to 10 micrometer wavelengths. Finally, PMTs are large, fragile, expensive and require high voltages to operate while solid state detectors are small, rugged and relatively inexpensive. In summary, the photo diodes outperform PMTs in most aspects other than built-in amplification by a wide margin.

SUMMARY

[0005] In an aspect of the disclosure, a

BRIEF DESCRIPTION OF THE DRAWINGS

{0006] FIG. 1A illustrates an optical transfer function (OTF) provided by a plane mirror standing wave microscope.

[0007] FIG. IB illustrates a point spread function (PSF) provided by the microscope of FIG. 1A.

[0008] FIG. 2 illustrates a conceptual omnidirectional standing wave microscope in accordance with an aspect of the disclosure.

[0009] FIG. 3 illustrates a conceptual processor system configured with the omnidirectional standing wave microscope of FIG. 2, in accordance with an aspect of the disclosure.

[0010] FIG. 4 illustrates a conceptual apparatus for super-resolution optical microscopy in accordance with an aspect of the disclosure.

[001 1] FIGS. 5A-5F illustrate the 3-D resolution enhancement that may be obtained in operation of a a OSW microscope equipped with an RDOE for super-resolution optical microscopy in accordance with an aspect of the disclosure. [0012] FIG. 6 is a flow diagram describing a method for obtaining an image using super- resolution optical microscopy in accordance with an aspect of the disclosure.

DETAILED DESCRIPTION

[0Φ13] Various aspects of the present invention will be described herein with reference to drawings that are schematic illustrations of idealized configurations of the present invention. As such, variations from the shapes of the illustrations as a result, for example, manufacturing techniques and/or tolerances, are to be expected. Thus, the various aspects of the present invention presented throughout this disclosure should not be construed as limited to the particular shapes of elements (e.g., regions, layers, sections, substrates, etc.) illustrated and described herein but are to include deviations in shapes that result, for example, from manufacturing. By way of example, an element illustrated or described as a rectangle may have rounded or curved features and/or a gradient concentration at its edges rather than a discrete change from one element to another. Thus, the elements illustrated in the drawings are schematic in nature and their shapes are not intended to illustrate the precise shape of an element and are not intended to limit the scope of the present invention.

[0014] It will be understood that when an element such as a region, layer, section, substrate, or the like, is referred to as being "on" another element, it can be directly on the other element or intervening elements may also be present. In contrast, when an element is referred to as being "directly on" another element, there are no intervening elements present. It will be further understood that when an element is referred to as being "formed" on another element, it can be grown, deposited, etched, attached, connected, coupled, or otherwise prepared or fabricated on the other element or an intervening element. In addition, when a first element is "coupled" to a second element, the first element may be directly connected to the second element or the first element may be indirectly connected to the second element with intervening elements between the first and second elements.

[0015] Furthermore, relative terms, such as "lower" or "bottom" and "upper" or "top," may be used herein to describe one element^'s relationship to another element as illustrated in the drawings. 2014/052589

It will be understood that relative terms are intended to encompass different orientations of an apparatus in addition to the orientation depicted in the drawings. By way of example, if an apparatus in the drawings is turned over, elements described as being on the "lower" side of other elements would then be oriented on the "upper" side of the other elements. The term "lower" can therefore encompass both an orientation of "lower" and "upper," depending of the particular orientation of the apparatus. Similarly, if an apparatus in the drawing is turned over, elements described as "below" or "beneath" other elements would then be oriented "above" the other elements. The terms "below" or "beneath" can therefore encompass both an orientation of above and below.

[0016] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and this disclosure.

[0017] As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprise," "comprises," and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. The term "and/or" includes any and all combinations of one or more of the associated listed items.

[0018] A structure and method is disclosed using photo-parametric amplification (PPA) to detect light in biomedical applications that use pulsed lasers for excitation.

[0019] Figure 1 is a conceptual representation of a system 100 for PPA sensing and/or imaging. Light 107 originates from a pulsed laser 104 and is directed mostly to an optical system 106. A small f action of the laser output 107 is diverted to a reference detector 108 that is used to synchronize a photo -parametric amplifier 110 to the laser 104. The reference signal is amplified P T/US2014/052589

and fed to a phase locked-loop circuit 112 that controls a voltage controlled frequency oscillator (VCO) 114 optimized for low phase noise and high spectral purity. It is understood that the noise of this VCO 114 may be limit the performance of the photo-parametric amplifier 110, hence a high quality VCO 114 is desirable. The phase locked loop (PLL) circuit 112 includes a variable delay mechanism 116 to adjust the phase of a pump signal 117 with respect to the laser output 107. The PLL circuit 112 includes a phase frequency detector (PFD) 118, a low pass filter (LPF) 120, the VCO 114 and a frequency divider (f/2) 122. Typically, this functionality may be integrated into one commercially available integrated circuit.

[0020] The laser light 107 may be passed through various optical filters (excitation filter 130 and/or emission filter 132) and is directed at a specimen 133 under investigation. By using a scanning mechanism 134, scanned point sensing may provide an image. The collected light from the specimen 133 under investigation is directed to the photo-parametric amplifier 110, where it may first pass through the emission filter 132, where the emission filter may include one or more spectrometers (not shown). As an example, in biomedical applications, the sensed light is not the light that was used to illuminate the specimen 133. Rather, processes such as fluorescence, secondharmonic generation, and Raman scattering may used to measure molecular properties of the specimen 133. The most common of these methods is the use of fluorescence from certain dye molecules that are attached to antibodies which in turn selectively bind to specific proteins, e.g., at specific sites. Thus the fluorescence light reports the location of the protein of interest. For this invention to be applicable to such indirect imaging methods, it is preferable that the periodic modulation of the excitation signal is preserved by the imaging process and is present in the emission signal. This is the case for the non-linear processes such as second-harmonic generation and Raman scattering. Furthermore, the fluorescent lifetime of most organic dyes is in the sub- 10 nano-second range, which means that the fluorescent signal from these dyes also retains most of the time varying structure of the laser illumination source 104. This also means that the practice of functional staining or labeling with green fluorescent proteins (GFP) can yield a signal that maintains the repetition frequency of the light source, [0021] It may be noted, however, that the details of the optical system 106, including the scanning mechanism 134 and the interaction of the excitation light 107 with the specimen 133 under investigation are immaterial to the disclosed- apparatus. They are mentioned to provide an example of a possible application. The key elements of the disclosed apparatus include the use of a periodically pulsed light source, such as the laser 104 and the photo-parametric amplifier PPA 110 that is synchronized to the repetition rate of the light source.

[0022] An example of the photo-parametric amplifier 110 is depicted in the circuit in Figure 2. As an example, the photo-parametric amplifier 110 was designed to operate at 40 Mhz to match the repetition rate of a Fianium Supercontinuum laser [Fianium.07], however, another amplifier speed may be designed to match another light source. In the example shown in FIG. 2, a light detector 205 is a C30971BFC fast silicon photodiode from Perkin Elmer, which is integrated into a fiberoptic FC-type connector. It should be noted that this is a typical silicon photodiode and not a varactor diode specifically designed for microwave applications. Hence the diode is optimized for light sensitivity and not for its controllable junction capacitance. The photodiode 205 may be optimized for speed, which means that the internal series resistance is low, which in turn reduces its Johnson noise contribution. However, when the photodiode 205 is operated in the photo- conduction mode, that is with a reverse bias applied, its shot-noise dominates.

[0023] An inductor LI and a capacitor CI form a high-Q resonator 210 circuit that resonates at 80 Mhz, and which is excited from the pump input 117 via a capacitor C3. One or more capacitors that make up C5 provide DC isolation of the pump-resonator 210 while blocking an RF signal path to ground. A connection B may be used to apply a reverse bias voltage to the photodiode 205 and also to measure the sum of a light induced DC photo-current and a dark current. The cathode of the photodiode is connected an inductor L2 and a capacitor C2, which form a LC-resonator 220 tuned to 40 Mhz. A case 230 of the photodiode 205 may preferably be grounded. The case 230 may be attached to RF-shielding (not shown) of the circuit. A signal from the resonator 220 may be coupled to the output of the PPA 110 via a capacitor C4. The entire PPA 110 may preferably be enclosed in an soldered RF-shield. The two tank circuits 210, 220 may preferably be located in separate shielded chambers and have very low inductive coupling. [0024] Controlling gain is important for biomedical applications, and because of the high sensitivity of the gain to the pump power level, it is preferable that the PPA 110 include facilities to control and stabilize the power of the input pump 117. In one implementation, the output of the VCO 114 is fed to a variable gain amplifier (VGA) 124 which in turn drives the PPA 110. A fraction of the pump input 1 17 power is diverted to a stable sensor to measure the power delivered to the PPA 110. This value is compared to gain setting and the difference is used to adjust the gain of the VGA by a gain control 140. This is a form of open loop stabilization that relies on measuring the relation between PPA gain and pump power and that assumes that this calibration remains stable.

[0025] For some critical applications, closed loop stabilization may be preferable because of the high sensitivity of the PPA gain to pump power and bias voltage. There are several methods that can be used to measure the PPA gain during operation: (a) Measure the shot-noise from the photo diode 205. The shot noise is proportional to the square-root of the sum of photo- and dark- current, which can be measured fairly easily. It has a broad spectral distribution that can be assumed to be uniform over the operating bandwidth. Thus, by measuring the signal strength of a narrow band just outside of the operating bandwidth and comparing that value to the expected noise for the actual photo diode current, a direct measure of the gain of the entire amplification chain is achieved; (b) Add an optical pilot signal. For example by adding a fiber-optic link between the photo diode 205 and a reference light source. The reference light source can be a stabilized light emitting diode. The reference light source adds a veiy small signal at a frequency that is just outside of the operating bandwidth. This signal is subsequently detected at the output of the amplifier chain via synchronous demodulation and provides a direct measure of the total gain of the entire amplifier chain. While the extra light will add some noise to the system, it also provides a direct, stable end-to-end measure and permits long-term, reliable calibration of the instrument; (c) Add an electronic pilot signal. This method is identical to the method described above, except that it uses a loosely coupled probe to inject the pilot signal electronically into the resonant circuit of the PPA 110. This approach has the advantage that it does not add noise to the system. It also has the disadvantage that it does not include a measure of the conversion efficiency of the photodiode, which will change slightly depending on device age and temperature. [0026] The gain of the PPA 110 also depends on the reverse bias of the photo diode 205. This bias voltage is essentially a mechanism to fine tune the PPA 110. The sensitivity of the PPA 110 on the bias voltage is modest; hence a digital to analog converter that produces 0-10V with 8 to 12 bits of resolution may be adequate. The PPA 110 performance can be optimized by changing the bias voltage depending on the pump-power level.

[0027] The overall sensitivity of the PPA 110 is limited by the dark current of the photodiode 205 and its associated shot noise. In order to achieve the full potential of this light detection system, it may be preferable to cool the photo diode 205. Because the photodiode 205 generates no significant amount of heat, a conventional thermoelectric cooler may suffice.

[0028] The gain of a degenerate parametric amplifier, such as the PPA 110 described in this disclosure is phase sensitive, which means that it may be necessary to adjust the phase of the pump oscillator with respect to the excitation pulses. Controlling the phase of a phase locked loop, such as the one described above is easily done using any of a plurality of standard solutions for this type of problem, including electronic phase shifters, variable delay element or direct digital synthesis (DDS) in the PLL loop. For example an AD9540 integrated circuit from Analog Devices may be considered a suitable element for this purpose.

[0029] The fact that the PPA 110 is phase sensitive is beneficial for this application because out-of phase noise is attenuated, which effectively halves the noise contribution of this detection system (110). In addition, varying the phase of the detection system deliberately can be used as a sensing mechanism to measure the fluorescent lifetime of a molecule that is being sensed. The lifetime information can be used to discriminate between several signals with otherwise similar optical properties.

[0030] The various aspects of this disclosure are provided to enable one of ordinary skill in the ait to practice the present invention. Modifications to various aspects presented throughout this disclosure will be readily apparent to those skilled in the art, applications to other technical ails, and the concepts disclosed herein may be extended to such other applications. Thus, the claims are not intended to be limited to the various aspects photo-parametric amplification presented throughout this disclosure, but are to be accorded the full scope consistent with the language of the claims. All structural and functional equivalents to the elements of the various aspects described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the claims. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the claims. No claim element is to be construed under the provisions of 35 U.S.C. § 1 12, sixth paragraph, unless the element is expressly recited using the phrase "means for" or, in the case of a method claim, the element is recited using the phrase "step for."

WHAT IS CLAIMED IS:

1. A solid state detection system comprising:

a degenerate photo-parametric amplifier (PPA), wherein the PPA comprises a photo diode; and

a periodically pulsed light source, wherein the photo-parametric amplifier (PPA) is synchronized to the pulsed light source with a phase locked loop that generates a pump waveform for the PPA at twice the frequency of the excitation pulse rate. . The system of claim 1, further comprising:

an automatic gain control system configured to adjust a level of power of the pump waveform based on measuring a photo-current and an intensity of shot noise of the photo diode within a narrow bandwidth of the PPA. . The system of claim 1, further comprising:

an automatic gain control system configured to adjust a level of power of the pump waveform based on measuring the signal from a small optical pilot signal directed at the photo diode, wherein the signal is sensed via a narrow-band, synchronous demodulation of the output from one of the PPA or a subsequent amplification stage. . The system of claim 3, wherein the small optical pilot signal is replaced by an electronically injected pilot signal. . The system of claim 1 , the phase lock loop comprising:

a variable delay circuit coupled to the periodically pulsed light source;

a phase frequency detector (PFD) coupled to the variable delay circuit;

a low pass filter coupled to the PFD;

a voltage controlled frequency oscillator (VCO) coupled to the low pass filter;

a frequency divider coupled to the VCO and the PFD; and

LA7480192.1 a variable gain amplifier (VGA) coupled to the VCO and the frequency divider. The system of claim 5, wherein the phase lock loop is coupled to the periodically pulsed light source via a reference detector. The system of claim 5, further comprising a gain control coupled to the VGA and the PPA. The system of claim 7, configured to provide light from the periodically pulsed light source to an optical system and to receive at the PPA light emitted from the optical system. The system of claim 1, further comprising a radio f equency (RF) amplifier coupled to the PPA to receive the The system of claim 5, wherein the variable delay circuit is coupled to the periodically pulsed laser source via a reference detector;

W 201

43 APPENDIX III

A method for generating Remote Synthetic Centers of Beam Rotation for

Software-Selectable Mating of Diverse Optical Systems

Andreas G. Nowatzyk, Robert G Chave, Daniel L. Farkas

The Brain Window, Inc.

ABSTRACT

A method is described for generating arbitrary centers of beam rotation in free space that permit the coupling of an optical system of arbitrary characteristics to a laser-detector assembly, or that adapt a pair of arbitrary optical systems to one another through software selectable modifications alone. This approach is of special interest for high-resolution retinal scanner for the early, low cost detection of Alzheimer's disease. Other applications of interest include coupling laboratory optical systems in situation where flexibility is of great importance and a time delay of some minutes in image transfer is acceptable. QUAD-GALVOS-SYNTHESIZED BEAM ROTATION/SCANNING

Understanding Controller Design Options with a mode! in Linear A!gebra

When the equations of motion for Nowatzyk's Quad Galvos are written a series of transformation matrices acting on the vector of the initial ray R0 emerging from the SCBR point several 'artifacts' of the configuration are evident. The most important of these is the following: among the four variables of mirror position α-ι through a₄ only C and ct₂ are fully independent variables.

This independence of α-ι and a₂ occurs when the other parameters of the configuration, such as the lengths between mirror centers, through L₄ are fixed into a specific QG 'design' optimized for factors such as the location SCBR relative to the QG and the available f-number. When these parameters are fixed mirror position angles i and a₂ become single valued functions of the angles Θο and γο. These are the angles that determine the position of the first ray R₀ to enter the mirror system starting from the SCBR point.

In this context Mirror positions a₃ and a₄ of the last two mirrors in the QG sequence are completely determined functions of the first two mirror positions. These dependencies permit the control system to be relatively simple. Mirror angles and ₂ are a function of R0 beam angles θ₀ and γ₀. Mirror angles a₃ and ct₄ are calculated from α-ι and a₂. Once an initial position is fixed, the relative locations of the mirrors are perturbations from this local datum. The result is very direct.

Algorithm for Determining MI: tor Positions

The following pages are of code from a program in MathCAD14 that solves for the independent mirror positions a_? and a₂, from inputs defining the source ray R_c. The two inputs Θ₀ and y₀ are shown in amber at the top, as are the four outputs show in amber at the bottom. Active portions of the code are shown in blue. The remaining dependent mirror positions a₃ and a₄ are calculated from the first two mirror positions, t and ₂.

While not all readers will follow every element of this code the MathCAD14 language has similarity to many programming languages. The point of including this code Is to demonstrate the relative directness the mirror angle calculation. Only a few lines of code are necessary to calculate and control a QG to maintain focus at the coordinates of an arbitrarily determined SCBR point.

Page 5 QUAD-GALVOS-SYNTHESIZED BEAM ROTATION/SCANNING

In a solution of the four mirror system which takes a ray from a focus at (0,0,0) through the

four reflections, exiting in a ray parallel to the y axis from the last mirror, the reflection from

mirror M3 is constrained to lie on a straight line, on the face of the mirror, which is also

parallel to the y axis. Given this constraint, two of the three coordinates of the point of

reflection Pr3 on M3 are defined by the coordinates of this y-axis parallel line at, Pr3x = L3

and Pr3z = L1. The third coordinate varies with the angular positions of M1 and 2. An

equation for Pr3y completes the set of constraints needed to define all four mirror angles.

Pr3 := L3 Pr3 := LI

In this four-mirror system only the angular positions first two mirrors M1 and M2 are

independent variables. The positions of mirrors IV13 and M4 are completely determined by the combined positions of M2 and M3. The incoming positions of R0 are 'givens'. The exiting

position of R3 is constrained by point P4_proj and f_plane. Given these two sets of

constraints the angular positions of M1 and M2 can now be determined.

Repeating the above calculations with the functions generated above, order order to put all the constraints on the angular positions of M1 and M2 inside a single numerical search 'solve block'.

Guess values for a 1 and a 2:

111

Defining Mirror Locations in terms of these trial values of a 1 and a 2

Page 8

The cross product at which the reflected ray off the second mirror and the vector determined by the

point will be zero at one unique set of positions of mirrors M1 and M2. Solving for these angles:

1111

Intersection point with Third Mirror

Normal to Third Mirror, which pivots about a Y axis

nominal starting position

w m i M

Page 7 QUAD-GAL VOS-SYN HESIZEIf BEAM ROTATION/SCANNING

R3(al,a2,a3) =

[-15 J

Illlliilii a3 =41.S72758deg

which pivots about an X axis

pos

0 )

<χφ>§ *sw«¾. I n(a4) -0.707107 |n4(a4)| =1

0.707107 J

Point on Fourth Mirror and Reflection Point on Third Mirror

nersec on pon w ou rror

a4 = 45-deg

al -· 3937275Sde

a2 = 45'ds^

«3 -41372758de

a4 = 4 -clej^

The case shown is the one in which Θ0 is 90 degrees. In this case only mirrors 1 and 3 are active.

The others sit at 45 degrees. Similarly when Θ0 is zero only mirrors 2 and 4 are active, and mirrors 1 and 3 sit at 45 degrees.

Paqe 8 Q D AD-G ALVOS-S YNTHES IZED BEAM ROTATION/SCANNING

Design & Configuration

The available field of view, whether or not a single SCBR is available or two, and the speed of the Quad Galvos in scanning the whole available field is highly dependent on mirror size and the center-to-center spacing of the mirror axes. Configuration of highly similar components for quiet varied applications is dependent on the adjustment of these two parameters: mirror size and center-to-center spacing.

Preliminary Design

The preliminary design based on Nowatzyk's original concept comprises a pair of two galvos based beam steering assemblies, mounted back to back. This is the design configuration shown below. This configuration is sufficient to demonstrate the concept. And the configuration may be assembled with off-the-shelf two galvos beam steering assemblies. Because the packing density off-the-shelf arrangement has been optimized for two rather than four galvos the possibilities from such configurations are limited.

Quad Gasvos System

figure 3

Page 9

Optimizing Mirror Packing

Application of CAD graphic models, showing the 'hard' dimensions of available actuator components in combination with CAD vector model described in the earlier sections of this report, reveal that much higher mirror packing densities are possible when a purpose built optical bench is used. There are commensurate increases in field of view.

The following image constructed in SolidWorks11 shows a Quad Galvos arranged for retinal scanning. The human eye shown in cross-section in the center lower right is to normal adult human scale with respect to the actuators.

Quad Galvos with Dense Packⁱng Configuration in Retina! Laser Scanning Application

Figure 4

Further contraction of the assembly is possible beyond that shown above. This is especially true when the travel of the galvos mirrors is limited from a normal 360 degrees of rotation, to only that motion necessary to achieve the scanning desired, When the constraint for 'whole turn' rotation is lifted, the edges of mirrors may be extended into what were previous dynamic envelopes save for unutilized ranges of motion. Constraining the 'whole turn' rotation requires only the inclusion of appropriate limit stops on the mirror axes themselves along with a concurrent limitation on the range of commanded motion from the controller.

^{" ' " """"} ~~ Page 10 QUAD-GALV OS-SYNTHESIZED BEAM ROTATION/SCANNING

Detailed view of Quad Galvos Retinal Scanning Configuration

Figure 5

Control Program Calibration

Control systems for scanning mirror assemblies tend to be based on the premise that axes of mirror rotation are truly orthogonal and that the mirror surfaces are identically the axes of rotation. In practice each axis will be slightly skew from an ideal coordinate reference frame. To obtain a system of the highest accuracy incorporating the tolerances of assembly into the control system is necessary. A non-contact method of identifying the as-built axes of the assembly in the final configuration of use is intended, such that these values may be entered into a 'look-up' table for the controller. The controller can then adapt to calculate each beam rotation based on the 'true' rather than the 'nominal' axis of each galvos mirror.

The need for axis correction emerges in other industries requiring the highest available precision. Notably, axis correction is a 'solved problem' in the world of industrial robot controllers. This is especially true in applications for which robot arms are used in semi-static mode for pick and place tasks requiring extremes of accuracy. The kinematic chain of a common robot arm and a Quad Galvos are similar in basic ways. The pivot bearings of both are nominally orthogonal. Errors in the bearings nearest the ground plane have a cumulative effect on the linkage further out. An approach¹ developed for KUKA robots at the Fraunhofer Gesellschaft IPK, Berlin is applicable for the QG case.

The calibration method is an iterative one. The method is one of taking the partial derivatives of the equations of end-effector (in this case projected exit beam) motion with respect to axis alignment; selecting cases in the range of permissible motion where the influence of one bearing axis is greater than others; approximating the axis error from that axis; inserting a corrective transformation matrix in the equation of motion, and repeating to convergence. For measuring KUKA robot arms a theodolite is used. With a Quad Galvos it is sufficient to project the exit beam to a targets located some meters distant.

' Fraunhofer-Ins tirut fur Produktionsanlagen und Konstruktionstechnik -IPK-, Berlin; Edited periodic progress report 1992 of ESPRIT project CAR-5220; "Data specification and structure to build a complete model for robot calibration"; Albright, S.L.; Schroer, K.

52 QDAD-GALVOS-SYNTHES1ZE BEAM ROTATION/SCANNING

Prior Art in Synthesized Rotation

The possibility of synthesizing a rotation in free space through the combined actions of rotations occurring elsewhere is such of fundamental utility that the existence of prior art of some type is almost inevitable. There is an invention that appears somewhat analogous to Nowatzyk's SCBR approach in the realm of kinematics and mechanisms theory. This is the 'remote centered compliance' (RCC) method of synthesizing a rotation off the body of a part, by using pivot points located on the part. This work was Daniel E. Whitney, at MITs Draper Labs.² An important distinction between the SCBR and the Whitey-RCC approach only approximates rotary motion about a remote point in free space. This is sufficient for a 'gripper' application in which the gripped part behaves as if it is being pulled at the remote center, not pushed. For the RCC to be effective approximate synthesized rotation is sufficient. The SCBR rotation, however, is not an approximation; it is exact.

Application of QQ Retinal Scanning to Early Detection of Alzheimer's Disease

An opportunity in the early detection of Alzheimer's disease through the retinal monitoring of β- amyloid (Αβ) plaques, the neuropathologicai hallmarks of Alzheimer's disease (AD). The images below show the relatively high contrast of this signal, which comes from the curcumin (from the culinary spice turmeric ginger family Zingiberaceae) label that attaches itself very specifically³ to the plaques Its florescence is in the visible range, detectable with current imaging technologies.

Scan of Αβ plaque fluorescence on a mouse Retina; Neuroimage. 2011 Jan;54 Suppl 1 :8204-17

Figure 6

² US Patent Number 4527557; The Charles Stark Draper Laboratory, Inc.; Daniel E. Whitney;

"A remote center compliance (RCC) gripper system including: an erectable RCC device including a compliance unit having a plurality of compliance members; and apparatus for applying a force to the centrally disposed joint to fix the joint and erect the RCC device." Filed April 23 1982.

³ Neuroimage. 201 1 Jan;54 Suppl 1 :8204-17. Epub 2010 Jun 13. "Identification of amyloid plaques in retinas from Alzheimer's patients and noninvasive in vivo optical imaging of retinal plaques in a mouse model." Koronyo-Hamaoui M, Koronyo Y, Ljubimov AV, Miller CA, Ko MK, Black KL, Schwartz M, Farkas DL; full paper: http://www.ncbi.nlm.nih.gov/pmcyarticles/PMC2991559/

Page 12 QUAD-GALVOS-SYNTHESIZED BEAM ROTATION/SCANNING

We (The Brain Window, Inc.) plan to build a new type of optical imaging instrument that would allow the (significantly weaker, visible wavelength) autofluorescence of β-amyloid (Αβ) plaques to report on their whereabouts, features and dynamics. In our estimate, this requires a multimode imaging approach, where all the main elements that determine the obtainment of a retinal image and its quality are re-examined and incorporated into the new instrument. These will not be detailed here, but we will stress that the new scanning options enabled by the quad galvos are one of several proprietary methods we intend to bring to this task.

The block diagram of the new instrument appears in Figure 7 below, with the quad ga!vos described above appearing in the green square block. aeousio-optieal

supcrcomnumm quad galvos

tunable filter

laser collimator beam splitter

low pass dichruic

fiber optic iced amplified diode dcieutor

Quad Galvos Based Retinal Scanner Block Diagram

?igure 7

Assembling a Prototype Scanner

The above is a block diagram summarizing the incorporation of our scanner into the complete instrument. The quad galvos is fiber fed from the broadband source. This reduces the weight and complexity of the hand held elements meaningfully. A Fianum "WhiteLase Micro" compact super- continuum fiber-fed laser produces useful power over 450 nm - 1800 nm range, averaging > 2 mW / nm. Pulsed around 40 MHz. A recent price reduction in this class of components for lower power applications makes them more commercially attractive.

Source: rianum Microiaser Inc., Marc^i 2012

f gure 8

Page 13 [054] The terms and expressions which have been employed in the foregoing specification are used therein as terms of description and not of limitation, and there is no intention, in the use of such terms and expressions, to exclude equivalents of the features shown and described or portions thereof, it being recognized that the scope of the invention is defined and limited only by the claims that follow.

Claims

1. A heterodyned interferometric fluorescence imaging method, comprising: providing a source of coherent light; producing from the source beam of coherent light a first illumination beam having a center wavelength and propagating along a first optical path and a second illumination beam having a center wavelength and propagating along a second optical path; shifting the relative center wavelengths of the first illumination beam and the second illumination beam a known amount; illuminating a sample with light from the first illumination beam and with light from the second illumination beam, the sample comprising fluorescent molecules that fluorescence light at a fluorescence wavelength in response to light from the first illumination beam and in response to light from the second illumination beam; and detecting the fluorescence light at a plurality of different locations.

2. The method of claim 1, further comprising identifying the location of a fluorescent molecule based on a pattern of detected fluorescence light.

3. The method of claim 2, wherein identification of the location of a molecule comprises collecting patterns of detected fluorescence light for a respective plurality of sample points in a sample space, performing an inverse Fourier transform on the collected patterns of detected fluorescence light to obtain a spatial density distribution of fluorescent molecules.

4. The method of claim 3, further comprising applying an inverse Radon transform to the density distribution to obtain a three dimensional image of the fluorescent molecules in the sample volume.