WO2008037007A1

WO2008037007A1 - Methods for optical microscopy

Info

Publication number: WO2008037007A1
Application number: PCT/AU2007/001423
Authority: WO
Inventors: Timothy Robert Hillman; Sergey Alexandrov; David Sampson; Thomas Gutzler
Original assignee: The University Of Western Australia
Priority date: 2006-09-25
Filing date: 2007-09-25
Publication date: 2008-04-03

Abstract

The present invention provides a method of generating a microscope image of an object using Fourier holography. The method comprises selecting a plurality of object angular or spatial frequency ranges for recording respective Fourier holograms of the object. The method also comprises recording the Fourier holograms for the respective object angular or spatial frequency range. Further, the method comprises generating the microscope image from a combination of the recorded Fourier holograms associated with the respective object angular or spatial frequency ranges. The object angular or spatial frequency ranges are selected so that each Fourier hologram has an object angular or spatial frequency range which has a portion that is in common with the object angular or spatial frequency range of another Fourier hologram.

Description

METHODS FOR OPTICAL MICROSCOPY

Field of the Invention

The present invention broadly relates to methods for optical microscopy. The present invention relates particularly to methods for generating a microscope image of an object using Fourier holography.

Background of the Invention

Optical microscopy is widely used for quality inspection and analytical procedures. Optical microscopes having objective lenses with high numerical apertures (NA) are used for generating high resolution images. Such high NA lenses are expensive and require very short working distances, such as 0.1mm, which is of significant disadvantage for inspection or analysis of objects having non-planar and structured surfaces. For example, biological objects often are non-planar and high resolution imaging of such objects is particularly cumbersome. Further, samples may be covered by glass slides, which makes imaging at very short working distances impossible. In addition, the field of view is relative small and an immersion medium typically is required, which is of added disadvantage.

There is a need for technological advancement.

Summary of the Invention

The present invention provides in a first aspect a method of generating a microscope image of an object using Fourier holography, the method comprising: selecting a plurality of object angular or spatial frequency ranges for recording respective Fourier holograms of the object; recording the Fourier holograms for the respective object angular or spatial frequency ranges; and generating the microscope image from a combination of the recorded Fourier holograms associated with the respective object angular or spatial frequency ranges; wherein the object angular or spatial frequency ranges are selected so that each Fourier hologram has an object angular or spatial frequency range which has a portion that is in common with the object angular or spatial frequency range of another Fourier hologram.

As the object angular or spatial frequency ranges are selected so that each Fourier hologram has an object angular or spatial frequency range which has a portion that is in common with the object angular or spatial frequency range of another Fourier hologram, the object angular or spatial frequency ranges "overlap", which facilitates positioning the Fourier holograms relative to each other for generating the microscope image.

The object angular or spatial frequency ranges typically are selected so that the overlapping Fourier holograms map a region of the object angular or spatial frequency space.

As the Fourier holograms are associated with respective object angular or spatial frequency ranges and the image is generated from a combination of the recorded Fourier holograms, it is possible to generate a synthetic aperture for the image that is larger than the numerical aperture associated with the recording of each individual Fourier hologram. Consequently, the optical element used for recording the Fourier holograms may have a relatively small numerical aperture and may be relatively inexpensive, even if the synthetic aperture is relatively large.

A relatively small numerical aperture has also the significant practical advantages that the working distance and field of view of an optical element, such as the working distance and field of view of a microscopy objective lens, may be relatively large. An immersion medium typically is not required and the working distance of a microscopy objective lens used for recording the Fourier holograms may be larger than 10mm, 20mm or even larger than 30mm. Such relatively large working distances are particularly advantageous for imaging non-planar objects and the above-defined method enables imaging such objects with relatively large synthetic apertures with a corresponding large field of view.

Because of the relatively small field of view associated with prior art methods, imaging of relatively large object areas typically requires recording multiple images. Even though generating an image having a large field of view using the above-defined method comprises recording a plurality of Fourier holograms, each recording typically is associated with the above-defined practical advantage of relative large working distance and there is no need for an immersion medium.

The object angular or spatial frequency range of the generated image typically is larger than the object angular or spatial frequency range of an image associated with the same field of view and obtained using a method different to that of the first aspect of the invention.

Further, the above-defined method enables generating images having a substantially constant contrast for a wide range of object angular or spatial frequencies. For example, it is possible to record the Fourier holograms for a wide range of spatial frequencies in a manner so that the contrast is substantially independent from the object angular or spatial frequency up to a spatial frequency of 2/λ (λ: wavelength of the radiation used for illumination of the object) which corresponds to a limit of resolution. In conventional incoherent microscopy the contrast is decreasing for increasing spatial frequencies and is zero at 2/λ. Consequently, the above-defined method offers improved resolution and enables identification of object features having a dimension that is smaller than the wavelength of the radiation used for recording the Fourier holograms.

The recorded Fourier holograms represent a recording of optical fields, which may be processed using various processing methods. Such processing methods may comprise comparing areas of the object, such as a pathological object or any other type of object, to identify relative differences between the areas, or comparing different objects. Further, the method may comprise comparing an area of the generated image at different times to identify relative differences as a function of time.

Selecting the respective object angular or spatial frequency ranges may comprise selecting respective wavelengths for the radiation used for illuminating the object. Alternatively or additionally selecting the respective object angular or spatial frequency ranges may comprise selecting at least one of: respective angular orientations of illumination relative to a surface of the object, respective angular orientations of a recording medium relative to radiation reflected or transmitted by object, respective solid angles of illumination, and respective solid angles of detection.

The object angular or spatial frequency ranges may be changed in an automated manner so that the image having a predetermined range of object angular or spatial frequencies can be generated in an automated manner.

The step of recording the Fourier holograms typically comprises illuminating the object with substantially monochromatic radiation, such as radiation provided from a Laser.

The step of recording the Fourier holograms typically also comprises recording the Fourier holograms using a two- dimensional recording medium. In this case the object angular or spatial frequency ranges are two-dimensional.

Alternatively, a three-dimensional recording medium may be used which enables three-dimensional recording of the Fourier hologram.

The object may be of any type including objects having relatively large surface height variations, any materials science objects, medical objects or biological objects such as cells and tissues. Any desired type of image may be generated from the same set of holograms, such as an image showing intensity distribution, quantitative phase, three-dimensional, or phase contrast/differential interference contrast or a combination thereof. For example, if a portion of the object is at least semi-transmissive for light, information for a region below the surface may be obtained by selecting a particular surface depth to be in focus, which typically comprises digitally processing a phase distribution associated with the recorded Fourier holograms.

Further, the above-defined method may be used for generating a three-dimensional image of a predetermined depth section of a structured object. In this case an illumination and reference radiation used for recording the Fourier holograms typically are non-monochromatic and provided by the same source. The predetermined depth section may be selected by effecting a relative difference in the optical path lengths between illumination and reference path. Within a depth section to which the recorded Fourier holograms correspond, a particular depth may also be selected by digitally processing a phase distribution associated with the recorded Fourier hologram. Consequently, it is possible to generate a three-dimensional image of the object with a strong axial sectioning capability. The thickness of the depth section typically is determined by a coherence length of the illumination and/or reference radiation.

In a first specific embodiment of the present invention the method comprises the additional step of and determining an angular light scattering distribution.

The step of determining an angular light scattering distribution typically comprises Fourier filtering the

Fourier holograms to select small angular ranges whereby a plurality of Fourier filtered holograms are generated that each correspond to a respective small angular range. Further, the step of generating the microscope image typically comprises generating the microscope image for a selected angular range, such as an entire angular range of recorded scattered light, for each small area of the object from a combination of microscope images that are associated with the respective small angular ranges. As the generated microscope image is a reconstruction of the object, it is then possible to identify the angular scattering distribution from each small area of the object within the selected angular range. The procedure may be repeated for other selected angular ranges.

In a variation of the above-described embodiment the Fourier holograms typically are not directly Fourier filtered prior to generation of the microscope image, but an area of the generated microscope image is selected and Fourier transformation of the generated microscope image is conducted for the selected area to obtain a map of angular light scattering distribution within a selected angular range, which is the entire angular range of recorded scattered light, for the selected area. A two- dimensional (inverse) Fourier transform operation may then be applied to the angular scattering spectrum power to detect a peak position and determine a size of an optical scatterer. This process may be repeated for any area of generated microscope image and any selected small angular range.

Suitable mathematical models can be applied to describe an associated optical scattering field (such as Mie or Rayleigh theory) . By analysing the light scattering distribution and comparing the determined light scattering distribution with theory, it is often possible to predict the presence of scattering particles that have a size that is below the spatial resolution of the image.

Alternatively, information about geometry and refractive index of the optical scatterers can be obtained.

The method according to the first specific embodiment of the present invention typically enables recording a light scattering distribution of an object over an angular range that is larger than that associated with the numerical aperture of the optical element used for recording the Fourier holograms. Further, the step of recording the

Fourier holograms may comprise recording both a spectral distribution of scattered radiation and an angular distribution of the scattered radiation, typically for each optical scatterer or for a group of scatterers simultaneously.

The present invention provides in a second aspect a method of recording a light scattering distribution of an object, the object comprising a surface portion that is at least semi-transmissive for light, the method comprising: selecting at least one first object angular or spatial frequency range for recording at least one Fourier hologram of the object; recording the at least one Fourier hologram for the respective object angular or spatial frequency range; selecting a depth into the surface portion of the object; calculating from the at least one recorded Fourier hologram a phase and amplitude distribution that is associated with the selected depth; generating the microscope image from the calculated phase and amplitude distribution; and determining an angular light scattering distribution for the selected depth of the object.

The method according to the second aspect of the present invention may also comprise the additional step of determining an angular light scattering distribution. Determining the angular light scattering distribution typically comprises applying Fourier filtering to the entire captured angular range, or Fourier transforming small selected areas of the reconstructed microscope image.

For example, it is possible to investigate the light scattering distribution for the selected depth. In addition another depth may be selected. The phase and amplitude may be calculated for the other depth and the light scattering distribution may then be investigated for the other depth. This process may be repeated for a number of selected depths and this way it is possible to obtain information about the light scatterer (eg size and/or refractive index) in three dimensions. Embodiments of the above-described method provide the ability to obtain information about a three dimensional structure even if only one Fourier hologram was recorded, which is particularly advantageous for studying a three-dimensional volume comprising small biological objects that frequently move.

The present invention provides in a third aspect a method of characterising an object that comprises, or is expected to comprise, a periodic structure, the method comprising: selecting at least two object angular or spatial frequency ranges that are associated with the period of the periodic structure; recording the at least two Fourier hologram for the respective object angular or spatial frequency ranges; and analysing if the obtained Fourier holograms are indicative of the period of the periodic structure.

The step of analysing may comprise analysing the recorded Fourier hologram directly. Alternatively, this step may comprise generating a microscope image from the recorded Fourier hologram and analysing the microscope image. The generated microscope image typically shows a significant change if there is an imperfection or interruption in the periodicity of the periodic structure. In addition, presence of the structure and its location within the object can be determined, even if the structure has a periodicity that is below the limit of resolution of conventional microscopy.

If the orientation of the periodic structure is known, a first Fourier hologram may be recorded for illumination from a first side of the structure and a second Fourier hologram may be recorded from an opposite side of the structure. The image is then generated to display the structure.

Embodiments of the method according the third aspect of the present invention enable characterising simple or complex periodic structures, for example for quality control in microelectronics and optics. For example, the object may be an optical grating having a high density of lines (for example 28800 lines/in) or the like, an integrated circuit or a mask that are produced using lithography and have very small features.

Imaging of such features using a conventional microscope would require scanning the entire object using an objective lens with a very high numerical aperture, which is very cumbersome especially because of the associated small field of view.

In one specific embodiment of the present invention the above-defined method is conducted so that analysis is possible substantially in real time and typically enables real time quality analysis. Sequences of such Fourier holograms may be taken for different regions of the object while the object is moving so that extended objects can be inspected.

In one specific embodiment the method in accordance with the third aspect of the present invention comprises selecting a plurality of object angular or spatial frequency ranges that are associated with expected respective periods of one or more periodic structures; recording Fourier holograms for each of the selected object angular or spatial frequency ranges; and analysing if the recorded Fourier holograms are indicative of at least one of the periods of the periodic structure.

The step of analysing typically comprises generating the microscope image from a combination of the recorded Fourier holograms and analysing the microscope image. In this embodiment the object angular or spatial frequency ranges typically are selected so that each Fourier hologram has an object angular or spatial frequency range which has a portion that is in common with the object angular or spatial frequency range of another Fourier hologram.

The object may be a structure that is expected to include a range of periodicities. By selecting corresponding object angular of spatial frequency ranges for recording the Fourier holograms, it is possible to determine that the periodicities are present and therefore verifying the quality of the object.

The present invention provides in a fourth aspect a method of generating a microscope image of an object that has a symmetric portion in a Fourier spectrum of the object, the method comprising: selecting at least one first object angular or spatial frequency range for recording at least one Fourier hologram of the object, the at least one first object angular or spatial frequency range being associated with the symmetric portion; recording the at least one Fourier hologram for the respective object angular or spatial frequency range; and generating the microscope image from the recorded Fourier hologram and incorporating a region that is symmetrical to a portion of the recorded Fourier hologram or the symmetrical portion of the corresponding spatial Fourier spectrum of the object.

For example, the region that is symmetrical to a portion of the recorded Fourier hologram, or the symmetrical portion of the corresponding complex spatial Fourier spectrum of the object, may be obtained by reflecting a portion of the recorded Fourier hologram about an origin.

The method according to the fourth aspect of the present invention may also include generating a second Fourier hologram for a second object angular frequency range that is associated with the symmetric region.

Incorporating the region that is symmetrical to a portion of the recorded Fourier hologram may be conducted numerically using suitable computer software.

The method typically comprises selecting a plurality of first object angular or spatial frequency ranges for respective Fourier holograms of the object, each first object angular or spatial frequency range being associated with the symmetric portion; recording the Fourier holograms for the respective object angular or spatial frequency ranges; and numerically generating a plurality of second Fourier holograms for second object angular or spatial frequency ranges that are associated with the symmetric portion and that differ from the selected first object angular or spatial frequencies; and generating the microscope image from a combination of the recorded Fourier holograms and the numerically generated holograms.

The following describes optional features that relate to each of the above-described embodiment of the present invention.

The object angular of spatial frequency ranges typically are two-dimensional object angular or spatial frequency ranges .

The generation of the microscope image may comprise processing the recorded Fourier holograms to select useful information, to correct for optical aberrations or for defocusing using suitable computer software routines. For example, the step of recording the Fourier holograms may be conducted so that the recorded Fourier holograms are out of focus. Such processing may also be conducted to improve the signal-to-noise ratio of the reconstructed image or prevent detector saturation. The step of generating the image may then comprise digitally refocusing the image. The step of generating the image may also be conducted so that differences in brightness, contrast or any other image properties are controlled.

The step of recording the Fourier holograms typically comprises recording the Fourier holograms digitally, for example using a CCD camera. Further, the method typically comprises the step of processing the digitally recorded Fourier holograms.

The present invention provides in a fifth aspect a device for generating a microscope image of an object using Fourier holography, the device comprising: a radiation source for illuminating an object; an optical system for generating a Fourier hologram of the object, the optical system being arranged so that optical conditions can be changed in a manner such that Fourier holograms associated with respective object angular or spatial frequency ranges can be generated; a recording medium for recording the Fourier holograms, the recording medium being positioned on an optical axis of the device; and computer software for processing the recorded Fourier holograms in a manner such that the microscope image of the object is generated from a combination of Fourier holograms associated with respective object angular or spatial frequency ranges.

The invention will be more fully understood from the following description of specific embodiments of the invention. The description is provided with reference to the accompanying drawings.

Brief Description of the Drawings

Figure 1 shows schematic representation of a device for generating a microscope image of an object using Fourier holography according to a specific embodiment of the present invention;

Figure 2 (a) - (c) illustrates the relative orientation of components of the device and the function of the device;

Figure 3 shows a plot of spatial frequency response versus spatial frequency for the device and for conventional microscopy techniques; and

Figures 4 to 6 illustrate processing steps used for processing recorded Fourier holograms according to specific embodiments of the present invention.

Detailed Description of Specific Embodiments

Referring to Figs. 1-3, a device and a method for generating a microscope image of an object using Fourier holography according to a specific embodiment of the present invention are now described.

Fig. 1 shows the device 100 and a sample 102. A light source (not shown) is used for generating an incident beam 104 that illuminates an object plane 101 of sample 102. A reflectance or transmittance configuration can be used. In this embodiment the incident beam 104 is a monochromatic beam and the source is a laser. Lenses 108 and 110 produce an image of the sample at image plane 106. A rectangular field stop (RFS) 112 is positioned at the image plane 106. A Fourier transform of the sample 102 is generated at Fourier plane 114. Lens 115 generates a further Fourier transform at a recording plane 116 of a CCD camera 118. A reference beam 120 is directed to the recording plane 116 of the CCD camera 118. The reference beam 120 has the same wavelength as the incident beam 104 and is generated by the same source. Interference of the Fourier transform of the sample with the reference beam 120 generates a Fourier hologram at the recording plane 116 of the CCD camera 118. The CCD camera 118 generates a digital recording of the Fourier Hologram.

The digital recording of the hologram is then processed using a suitable software routine. For example, the digital recording of the Fourier hologram may be corrected for aberrations or defocusing using the suitable software routine. The software routines are also used to generate an image of the sample or the angular/spectral distribution of scattered light for each local area of the sample from the recorded Fourier hologram or from a combination of recorded Fourier holograms. An example of processing steps involved in generating the image from Fourier holograms is given in the Appendix.

It is to be appreciated by a person skilled in the art that the above-described device 100 is only one example of many different arrangements which can be used for recording a Fourier hologram of a sample.

Fig. 2 (a) - (c) illustrates the relative orientation of components of the device 100 and illustrates the operation of the device. Fig. 2 (a) shows the plane 101 at which the sample 102 is positioned. The plane 101 with the sample 102 which are illuminated by the beam 104. The propagation direction of the beam 104 forms an angle of θi with a normal of the surface of the sample 102. Further, the propagation direction of the beam 104 forms an angle of Φi relative to an axis η of an f/yz-coordination system. The xyz-coordination system shown in Fig. 2 (b) corresponds to an optical Fourier transform of the z- coordination system shown in Fig. 2 (a) . Fig. 2 (b) shows the recording plane 116 of the CCD camera 118 which is illuminated by the reference beam 124. The propagation direction of the reference beam 124 forms an angle θ_r with a z-axis of the xyz-coordination system.

Fig. 2 (c) shows the sample 102 which is illuminated by the beam 104 at the angle of θi. Radiation is reflected from the surface of the sample 102 and detected at a detection angle α_out and a solid angle 128.

Fig. 2 (d) shows two-dimensional spatial frequencies v_η and Vξ. The two-dimensional spatial frequency range which corresponds to a recorded Fourier hologram is dependent on Φif ciout/ θi, the solid angle of detection, the solid angle of illumination and the wavelength of the illumination beam 104. Changing any one of these parameters changes the two-dimensional spatial frequency range that is associated with a recorded Fourier hologram. Fig. 2 (d) schematically indicates four areas of spatial frequencies which relate to four respective recording conditions.

After recording a first Fourier hologram using a set-up that results in a two-dimensional frequency range 130, the sample was rotated about a surface normal by 90° which resulted in a two-dimensional spatial frequency range 132. Fourier holograms corresponding to the spatial frequency ranges 134 and 136 were recorded in a corresponding manner. It will be appreciated by a person skilled in the art that alternatively the sample may be rotated by any other angle. Changing the angle θi or changing the wavelength of the illumination beam 104 changes the distance of the two-dimensional spatial frequency range from the origin of the plot shown in Fig. 2 (d) .

Each of the two-dimensional spatial frequency ranges indicated in Fig. 2 (d) , for example the spatial frequency range 130, corresponds to a respective set-up of the device 100 and to a spatial frequency range associated with the numerical aperture of an objective lens used for recording the Fourier hologram. If a number of such Fourier holograms, each having respective two-dimensional frequency ranges, are combined, an image can be generated that corresponds to a synthetic aperture which is much larger than the numerical aperture associated with each recording. Consequently, it is possible to use an objective lens having a relatively small aperture, and a corresponding advantageous large working distance, and generate an image having details and resolution that corresponds to an image obtained using a much larger numerical aperture. The advantages of high resolution, wide field of view and long working distance can be combined by the apparatus 100 and the above-described method. Further, imaging of surfaces having a large height variation at high resolution is facilitated.

The Fourier holograms are recorded so that each Fourier hologram has an object angular or spatial frequency range which has a portion that "overlaps" the object angular or spatial frequency range of an adjacent Fourier hologram. The "overlapping" provides the significant practical advantage that accurate positioning of the Fourier holograms relative to each other for image generation is facilitated.

The Fourier holograms may also be corrected for a relative phase off-set. Relative phase off-sets may be calculated from digital analyses of those regions of the Fourier holograms, which correspond to the overlapped spatial frequency ranges.

In a variation of the above-described embodiment of the present invention, the described method may also be used for inspection of a periodic structure. For example, an optical grating or another periodic structure, such as a mask produced by lithography and having very small features, may be moved relative to the illumination beam 104. The expected periodicity of the periodic structure may be known and corresponds -to a frequency within a predetermined two-dimensional frequency range. The device 100 may now be adjusted so that one or more Fourier holograms that correspond to that predetermined two- dimensional spatial frequency range are recorded.

If the orientation of the periodic structure is known, a first Fourier hologram may be recorded for illumination from a first side of the structure and a second Fourier hologram may be recorded for illumination at the same angle of incidence from an opposite side of the periodic structure. If the orientation of the structure in unknown, a number of holograms for differing illumination orientations are typically recorded.

The generated Fourier holograms may be analysed directly. Alternatively, the generated microscope image may be analysed, which typically includes numerical processing of the Fourier holograms to form complex Fourier spectra of the periodic structure (including both, positive and negative parts of the Fourier spectrum; calculated Fourier holograms may also be obtained using the symmetry of the structure from recorded negative or positive Fourier holograms, respectively, and then inverse Fourier transform to reconstruct the microscope image.

The object may move relative to the illumination beam 104 and the method typically is conducted so that a change in the periodicity of the periodic structure will then be apparent in the reconstructed image while the sample moves .

In a further variation of the above-described embodiment of the present invention, the described method may also be used for generating a three-dimensional image of a predetermined depth section of a structured object. In this embodiment the illumination and reference radiation used for recording the Fourier hologram are both non- monochromatic and are generated by the same source and the optical length of an object and reference path are matched. A depth section to which the recorded Fourier hologram corresponds is selected by selecting a relative difference in the optical path lengths between illumination and reference path.

Fig. 3 shows a plot of spatial frequency response versus spatial frequency for the device 100 and for conventional microscopy techniques. The limit of resolution of conventional coherent microscopy (dotted line, "coherent transfer function modulus") is 1/λ (λ: wavelength of light used for illumination) and conventional incoherent microscopy (dashed line, "modulation transfer function") has a spatial frequency response that gradually decreases to zero at 2/λ . The above-described method according to a specific embodiment of the present invention enables imaging of an object with a constant spatial frequency response up to the limit of resolution of 2/λ (solid line, "synthetic coherent transfer function modulus") . Because of the constant spatial frequency response, it is possible to image a microstructure having a size of λ/2 with relatively high contrast, which results in images having a resolution that is superior compared with that of images generated by conventional microscopy.

The following will describe an embodiment of the present invention that is useful for imaging objects that have symmetrical portions in their Fourier spectrum. In this embodiment a single Fourier hologram may be recorded in the above-described manner for an object angular or spatial frequency range. Using the laws of symmetry, a second Fourier hologram for another object angular or spatial frequency range may be generated numerically. The microscopy image is then generated from both the recorded and the calculated Fourier holograms and typically has a resolution that is superior to that of a microscope image that was generated from the recorded Fourier hologram only.

A person skilled in the art will appreciate that in the above-described embodiment alternatively more than one Fourier hologram may be recorded for respective object angular or spatial frequency ranges or more than one Fourier hologram may be generated numerically.

A further specific embodiment of the present invention is now described. In this embodiment the recorded Fourier holograms are analyzed to determine an angular scattering distribution of an optical scatter. For this purpose one or more Fourier holograms are recorded. Fourier filtering techniques are then used to select small angular ranges. A microscope image for a selected angular range is then generated from a combination of microscope images that correspond to respective small angular ranges. By studying the generated microscope image it is possible to identify an angular distribution from each area of the object. This way it is possible to determine the light scattering distribution form any areas of the object.

In a variation of the above-described embodiment the Fourier holograms typically are not directly Fourier filtered prior to generation of the microscope image, but an area of the generated microscope image is selected and Fourier transformation of the generated microscope image is conducted for the selected area to obtain a map of light scattering distribution within a selected angular range for the selected area. A two-dimensional (inverse) Fourier transform operation is then applied to the angular scattering spectrum power to detect a position of a peak corresponding to a structure in the angular scattering power and a determine size of an optical scatter. This process may be repeated for any area of generated microscope image and any selected small angular range.

For example, the object may contain very small optical centers. Suitable theoretical models can then be used to analyze the detected angular light scattering distribution and such analysis typically results in information about the light scatters such as refractive index and/or size of particles. This way particles may be detected that have a size which is well below the resolution of the microscopy image .

Further, a light scattering distribution for a particular depth of an object may be determined. For example, the object may include optically transmissive surface portions and light may be detected from subsurface regions. Since each recorded hologram includes phase and amplitude information, it is possible to calculate the phase and amplitude that corresponds to a particular depth below the surface. Such amplitude and phase information can be calculated for a sequence of layers, which enables to provide three dimensional information.

A person skilled in the art will appreciate at the light scattering distribution may be determined for any area or depth of the object from which light was received for recording the Fourier holograms. The obtained scattering distribution may be analysed as described in a publication entitled "Spatially resolved Fourier holographic light scattering angular spectroscopy", Sergey A. Alexandrov, Timothy R. Hillman, and David D. Sampson, Optics Letters, Vol. 30, Issue 24, pp. 3305-3307 and in a publication "Microscopic particle discrimination using spatially- resolved Fourier-holographic light scattering angular spectroscopy", T. R. Hillman, S. A. Alexandrov, T. Gutzler, and D. D. Sampson, Optics Express, 2006, v. 14, N 23, p. 11089-11102. The references that are made to these publications does not constitute an admission that the publications are a part of the common general knowledge in Australia or in any other country.

The following appendix relates to all previously described embodiment of the present invention and illustrates one possible computer software supported processing procedure that may be used for processing the recorded Fourier holograms. It is to be appreciated, however, that numerous variations of the now described procedure are possible.

Appendix A MATLAB procedure for processing the holograms may be described as follows:

Step 1: The initial parameters required to process the holograms are loaded (stored in the structured array CurrVals) . The following variables are added to it:

Wavelength: Illumination wavelength λ (possible value, 632.8xlO^"9m) fl: Lens 1 focal length / (0.015m) f2: Lens 2 focal length /₂ (0.15m) f3: Lens 3 focal length /₃ (0.26m)

Thetal: Incident wave polar angle O₁ (48.5°) Phil: Incident wave azimuthal angle φ_{ (51°)

Deltar: Distance between (or length of) square pixels in CCD array Δr (4.65xlO^~6m)

Step 2: The hologram file is loaded as a MATLAB array, in addition to reference and sample files if they exist. A "Processed hologram" array is generated, equal to the hologram minus the reference and sample waves.

Step 3:

Calculated (auxiliary) variables are stored in the structured array AuxVar. They are:

NH: Number of pixels in the vertical (height) direction of the hologram N₁₁ (and thus the y direction; see Fig. 2 (b) ) NL: Number of pixels in the horizontal (length) direction of the hologram N₁ (and thus the x direction; see Fig. 2 (b) )

H: Length of recorded region in vertical (and thus y, height) direction

L: Length of recorded region in horizontal (and thus x, length) direction ThetalRads: Incident wave polar angle θ_t in radians

PhilRads: Incident wave azimuthal angle φ, in radians

AlphaX: Parameter a_x = ^ύ*^θ>→^>

„. , , sinAsinώ, AlphaY: Parameter a_γ = '^■ ^

M: Parameter M =&&-

Step 4:

A figure is generated which shows the region of the sample spatial frequency plane that is recorded in the hologram.

Step 5:

The processed (and other) images are oriented

(aligned) so that increasing row number corresponds to increasing x value, and increasing column number corresponds to increasing y value.

The row and column coordinates of the array are thus:

L-Ar . L-Ar Row x values: :Δr: Column y values: .Ar: .

2 2

Fig. 4 shows the orientation of the matrix and the coordinate axes in Matlab after the transformation. The crosses indicate the centres of the (square) pixels.

Step 6:

A minimum k is chosen such that 2* is greater than or equal to both the number of rows and the number of columns in the array.

Step 7:

The "ProcessedΗologram" array is zero-padded to form a 2* x2* expanded array, "ExpandedArray", such that the original array is centred in it.

Row x values ("ExpandedXValues") : -(2^k'] -^)Ar:Ar:(2^k'] -^)Ar Column y values ("ExpandedYValues") : -(2*^"1-±)Δr:Δr:(2*^"'-^)Ar ExpandedArray is shown in a figure.

Step 8:

To apply the ifft2 algorithm, it is necessary that the origin of the system be located at the centre of a pixel. Therefore, we define an alternate set of coordinate axes (x",y") by translating the original (x,y) axes by a distance Δ/72 in both directions.

Fig. 5 shows an alternative coordinate axes set used for ifft2 algorithm:

Row jc" values: -2*^~'Δr:Δr :(2*^"' -1 )Δr Column y" values: -2*^"1Δr:Δr:(2*^"1 -I)Ar

The inverse Fast Fourier Transform (iFFT) algorithm may then be performed in Matlab, specifically: (Δr*2*)^Λ2 * fftshift( ifft2 ( fftshift ( . ) ) ) The result is then stored in the structured array ReconsRegion as Reconstruction. The spatial frequency variable in the transform domain v_x and v_γ coordinates for this resulting array are:

1 1 (2*-'-l) Row v_χ values: :—-—:-— -

2Ar 2^k Ar 2^k Ar

1 1 (2" - I)

Column v_γ values : : —. — : — -,

2Δr 2^kAr 2^kAr

They are stored in ReconsRegion as NuXValues and NuYValues respectively.

Step 9:

The array "Reconstruction" is multiplied by the factor exp{+jπAr(y_x + v_γ)} to compensate for the coordinate axes translation of step 9 (see Fig. 5) . The result is now F^~}\I_p(x,y) } . The row V_x values and column v_Y values are the same as they were in the previous step.

Step 10:

Figures are then displayed, which show the amplitude and the phase of ReconsRegion. Reconstruction, and they are titled "Fig04_ReconsMag_NuX_NuY_InvFT" and

"Fig05_ReconsPhase_NuX_NuY_InvFT" respectively. Users are asked to select a region for magnification and a "centre" point, corresponding to the point (-β_x,-β_Y) , the point to which the origin of the reconstructed sample is translated due to the direction of propagation of the reference wave. The magnified region and the values of θ_r,φ_r determined by the user's selections are displayed on the plots. The following variables are stored in the structured array AuxVar .

r, sin θ cos φ

BetaX : Parameter B_x = ^r- ^ and x λ o sin#_r sind_r

BetaY : Parameter β_γ = - ⁵^ . λ

ThetaRRads : Polar reference angle θ_r (determined by user choice of {-β_x,-β_γ)) PhiRRads: Azimuthal reference angle φ_r (determined by user choice of (-β_x,-β_γ))

ThetaR: Polar reference angle θ_r (in degrees) PhiR: Azimuthal reference angle φ_r (in degrees)

A new structured array is generated, MagRegion, to store information about the magnified region. The following variables are stored in the array:

MinNuY: Minimum value of v_γ in magnified region MaxNuY: Maximum value of v_γ in magnified region

MinNuX: Minimum value of V_x in magnified region

MaxNuX: Maximum value of v_x in magnified region

Step 11:

The array ReconsRegion. Reconstruction is cropped to yield only pixels contained within the magnified region. It is stored as MagnifiedRegion in the structured array MagRegion. The values for V_x and v_γ corresponding to this region are also stored in MagRegion, as vectors TransNuXValues and TransNuYValues respectively, however, as suggested by their titles, they have included the translation by (β_χ,β_τ) . The structured array ReconsRegion is saved in the .mat file "ReconstructedRegion" and cleared from memory. Two additional variables are stored in the structured array MagRegion. They are RecPercl and RecPerc99, which represent the 1^st and 99^th percentile values of the magnitude of MagnifiedRegion, and are used as bounding values on the colour map when plotting it.

Step 12:

A new array is generated by resampling

MagRegion. MagnifiedRegion at different V_x and v_γ values, chosen so that the number of each are equal, and a power of 2. Additionally, the pixel corresponding to

is immediately below (and to the right of) the centre of the new array (so that exactly half of the V_x and v_γ values are negative, and one less than half of them are positive) . The increment (distance between successive values) in both the V_x and v_γ directions is titled "Increment". In addition, two limiting magnitudes ResMag. LowColorbarVal and ResMag.HighColorbarVal are defined to be equal to MagnifiedRegion. RecPercl and MagnifiedRegion. RecPerc99 respectively.

Step 13:

Two movies are generated which show the result of correcting for output plane defocusing by multiplying the current reconstructed sample field R_λ(v_x,v_γ) by a quadratic phase factor H_d(v_x,v_γ) (representing propagation over distance d under Fresnel propagation) for several different possible values of the defocus distance d. One shows the phase of MagRegion.MagnifiedRegion as the quadratic phase shift is applied, and the other ("FourierPlaneMovie_d") shows the Fourier transform of ResMag.MagnifiedRegion after the quadratic phase shift. (It is not necessary to use the resampled magnified region of step 12 for the first movie, when no Fourier transform operation is applied. ) The varying value of d is displayed prominently in each movie frame. By viewing both movies, the user can decide when the apparent quadratic image phase structure is minimised (in the first case) , or when the image is best focused (in the second case) , thus determining the corresponding value of d, which will ideally be a good approximation of the true value.

Step 14;

The user is asked to enter the value of d in centimetres, based on examining the movies generated at the previous step (it may be known by any other means) . It is converted to metres and stored. The stored value

"ResMag.MagnifiedRegion" is corrected for recording plane defocusing, and a Figure is generated.

Step 15: A movie is generated showing the effects of focusing/defocusing in the sample plane (i.e., as a focusing distance g is varied) . The array "ResMag.MagnifiedRegion" is Fourier-transformed, divided by a g-dependent quadratic phase factor, and then inverse Fourier transformed. The magnitude of the resulting image constitutes a frame of the movie, with the corresponding value of g prominently displayed. By viewing the movie, and determining for which value of g the features appear sharpest, an appropriate defocus distance can be determined.

Step 16: The user is asked to enter the value of g in millimetres, which may be determined from the movie at the previous step. It is converted to a value in metres, and stored. By applying the steps outlined in the previous step (performing the Fourier-transform, dividing by the g- dependent quadratic phase factor, and then inverse Fourier transforming) , an updated version of "MagnifiedRegion" is generated. It is stored in the structured array "DefocusCorrect", as are the vectors "TransNuYValues" and "TransNuXValues" (identical to their values in the structured array "ResMag") . The stored values "DefocusCorrect . LowColorbarVal" and

"DefocusCorrect .HighColorbarVal" are determined by taking the 1^st and 99^th percentile values of the magnitude of "DefocusCorrect .MagnifiedRegion". The structured array "ResMag" is saved in the .mat file

"ReconstructedMagnifiedRegion" and cleared from memory. Figures are generated utilising the "DefocusCorrect" values instead of "ResMag" ones. In this step, the user is also asked to select a "Processing region", by selecting a series of points that they wish to be included in a magnified region of the image. The smallest rectangle (with a certain orientation) containing all of these points will be considered the "Process region". The orientation is, by default, vertical/horizontal, but the user is invited instead to click on a series of points to outline a grid as shown in Fig. 6. The points are be clicked in the order 1-16, and the vertices of the 3*3 square grid will be chosen to minimise the sum of squared distances between the chosen points and the fitted vertices. The rotation angle (shown to be a positive, acute value) is shown, and the line (1) - (2) - (3) - (4) will be displayed as a horizontal line in the rotated magnified "Process Image".

Step 17:

If no rotation angle was selected in the previous step, this region is merely a subregion of "DefocusCorrect .MagnifiedRegion"; otherwise, the values must be sampled (and interpolated) from "DefocusCorrect . MagnifiedRegion" . Variables "TransNuXValues" and "TransNuYValues" are also stored in the structured array "ProcRegion" . If no rotation angle was selected, they are the values they were in the previous step (merely cropped from their original vectors) . Otherwise, they are both chosen with a minimum value 0. In the structured array "ProcRegion", variables "LowColorbarVal" and "HighColorbarVal" are chosen, equal to their values in "DefocusCorrect". Figures are generated, displaying the amplitude and phase of "DefocusCorrect . MagnifiedRegion" .

Step 18: The process region is resampled at a sufficiently high spatial frequency in order to display the high- frequency carrier wave necessary to reconstruct the sample spatial frequencies. The default resampling frequency is taken to be twice the minimum value required to satisfy the Nyquist criterion with respect to the maximum of Ma_x or Ma_γ , i.e. the default resampling increment is min{\/(4Ma_x),\/(4Ma_Y)} . The user is asked to enter a "Process image resampling factor", which is multiplied by the default sampling frequency to give the final sampling frequency used. (For example, if the user enters the value 2, the default resampling increment will be min(1/(8MQr_xXlZ(SMaTy)J . Division by the carrier factor jexp{j2πM(v_xa_x+v_xa_γ)} is carried carried. After resampling, new values of "TransNuXValues", "TransNuYValues", and "ProcessingRegion" are stored in the structured array "ResProcRegion", as well as "LowColorbarVal" and "HighColorbarVal", which are set to be equal to their values in the structured array "ProcRegion". The structured array "ProcRegion" is saved in the .mat file "ProcessedRegion", and cleared from memory, and Figures are generated, showing, as before the magnitude and phase of "ResProcRegion . ProcessingRegion" .

Step 19:

The coordinate system of "ResProcRegion" is scaled and the coordinates labelled (ξ, η) (instead of (y_x,v_γ)) to yield the variables "XiValues", "EtaValues", "ProcessingRegion", "LowColorbarVal", and

"HighColorbarVal", stored in the structured array "ScaledProcRegion". (The latter two variables are equal to their values in the structured array "ResProcRegion".)

The process to the end of Step 19 describes the reconstruction of the sample profile from a single hologram. A reconstruction based on multiple holograms can be obtained by adding the reconstructed sample profiles due to each. If there is significant overlap between the holograms, or it is necessary to correct for possible relative phase errors, the holograms may be recombined in the frequency domain. That is, the final reconstructions may be Fourier-transformed, then aligned and added in the Fourier domain, before inverse-Fourier- transforming the resultant sum to yield the synthesised image .

Although the invention has been described with reference to particular examples, it will be appreciated by those skilled in the art that the invention may be embodied in many other forms. For example, it is to be appreciated that in alternative embodiments two- dimensional or three-dimensional Fourier holograms may be recorded which are associated with a range of spatial frequencies in three-dimensional space

Claims

The Claims ;

1. A method of generating a microscope image of an object using Fourier holography, the method comprising: selecting a plurality of object angular or spatial frequency ranges for recording respective Fourier holograms of the object; recording the Fourier holograms for the respective object angular or spatial frequency ranges; and generating the microscope image from a combination of the recorded Fourier holograms associated with the respective object angular or spatial frequency ranges; wherein the object angular or spatial frequency ranges are selected so that each Fourier hologram has an object angular or spatial frequency range which has a portion that is in common with the object angular or spatial frequency range of another Fourier hologram.

2. The method of claim 1 wherein selecting the respective object angular or spatial frequency ranges comprises selecting at least one of: respective wavelengths for the radiation used for illuminating the object, respective angular orientations of illumination relative to a surface of the object, respective angular orientations of a recording medium relative to radiation reflected or transmitted by object, respective solid angles of illumination, and respective solid angles of detection.

3. The method of claim 1 or 2 wherein recording the Fourier holograms comprises illuminating the object with substantially monochromatic radiation.

4. The method of any one of the preceding claims wherein recording the Fourier holograms comprises recording the Fourier holograms using a two-dimensional recording medium.

5. The method of any one of the preceding claims wherein the object is at least semi-transmissive for light and information for a region below the surface is obtained by selecting a particular surface depth to be in focus, which comprises digitally processing a phase distribution associated with the recorded Fourier holograms.

6. The method of any one of the preceding claims wherein the method is used for generating a three-dimensional image of a predetermined depth section of a structured object .

7. The method of claim 6 wherein an illumination and reference radiation are used for recording the Fourier holograms and which are non-monochromatic and provided by the same source and wherein the predetermined depth section is selected by effecting a relative difference in the optical path lengths between illumination and reference path.

8. The method of claim 6 wherein a predetermined depth is selected by digitally processing a phase distribution associated with the recorded Fourier holograms.

9. The method according to any one of the preceding claims wherein the method comprises that additional step of determining an angular light scattering distribution.

10. The method of claim 9 wherein the step of generating the microscope image comprises Fourier filtering to generate Fourier holograms for small angular ranges of scattered light and generating the microscope image for a selected angular range for each small area of the object from a combination of microscope images that are associated with the respective small angular ranges.

11. The method of claim 10 wherein the selected angular range for which the microscope image is generated is the entire angular range of recorded scattered light.

12. The method of claim 9 wherein an area of the generated microscope image is selected and Fourier transformation of the generated microscope image is conducted for the selected area to obtain a map of angular light scattering distribution within a selected angular range, which is the entire angular range of recorded scattered light, for the selected area.

13. The method of any one of claims 9 to 12 wherein analysis of the angular light scattering distribution for the selected area comprises comparison with theoretical models of the light scattering distribution.

14. The method of claim 9 wherein analysis of the angular light scattering distribution for a selected area comprises a two-dimensional (inverse) Fourier transformation operation applied to angular scattering spectrum power to detect a position of a peak corresponding to a structure in the angular scattering power.

15. A method of recording a light scattering distribution of an object, the object comprising a surface portion that is at least semi-transmissive for light, the method comprising: selecting at least one first object angular or spatial frequency range for recording at least one Fourier hologram of the object; recording the at least one Fourier hologram for the respective object angular or spatial frequency range; selecting a depth into the surface portion of the object; calculating from the at least one recorded Fourier hologram a phase and amplitude distribution that is associated with the selected depth; generating the microscope image from the calculated phase and amplitude distribution; and determining an angular light scattering distribution for the selected depth of the object.

16. A method of characterising an object that comprises, or is expected to comprise, a periodic structure, the method comprising: selecting at least two object angular or spatial frequency ranges that are associated with the period of the periodic structure; recording the at least two Fourier hologram for the respective object angular or spatial frequency range; and analysing if the obtained Fourier holograms are indicative of the period of the periodic structure.

17. The method of claim 16 wherein the step of analysing comprises analysing the recorded Fourier holograms directly.

18. The method of claim 17 wherein the step of analysing comprises generating a microscope image from the recorded Fourier holograms and analysing the microscope image.

19. The method of any one of claims 16 to 18 wherein the method is conducted so that analysis is possible substantially in real time and enables real time quality analysis .

20. The method of any one of claims 16 to 19 comprising selecting a plurality of object angular or spatial frequency ranges that are associated with expected respective periods of one or more periodic structures; recording Fourier holograms for each of the selected object angular or spatial frequency range; and analysing if the recorded Fourier holograms are indicative of at least one of the periods of the periodic structure.

21. The method of claim 20 wherein the step of analysing typically comprises generating the microscope image from a combination of the recorded Fourier holograms and analysing the microscope image.

22. The method of claim 20 or 21 wherein the object angular or spatial frequency ranges are selected so that each Fourier hologram has an object angular or spatial frequency range which has a portion that is in common with the object angular or spatial frequency range of another Fourier hologram.

23. A method of generating a microscope image of an object that has a symmetric portion in a Fourier spectrum of the object, the method comprising: selecting at least one first object angular or spatial frequency range for recording at least one Fourier hologram of the object, the at least one first object angular or spatial frequency range being associated with the symmetric portion; recording the at least one Fourier hologram for the respective object angular or spatial frequency range; and generating the microscope image from the recorded Fourier hologram and incorporating a region that is symmetrical to a portion of the recorded Fourier hologram or the symmetrical portion of the corresponding spatial Fourier spectrum of the object.

24. The method of claim 23 wherein the region that is symmetrical to a portion of the recorded Fourier hologram, or the symmetrical portion of the corresponding complex spatial Fourier spectrum of the object, is obtained by reflecting a portion of the recorded Fourier hologram about an origin.

25. The method of claim 23 comprising generating a second Fourier hologram for a second object angular frequency range that is associated with the symmetric region.

26. The method of claim 23 comprising selecting a plurality of first object angular or spatial frequency ranges for respective Fourier holograms of the object, each first object angular or spatial frequency range being associated with the symmetric portion; recording the Fourier holograms for the respective object angular or spatial frequency ranges; numerically generating a plurality of second Fourier holograms for second object angular or spatial frequency ranges that are associated with the symmetric portion and that differ from the selected first object angular or spatial frequencies; and generating the microscope image from a combination of the recorded Fourier holograms and the numerically generated holograms .

27. The method of any one of the preceding claims wherein the object angular of spatial frequency ranges are two- dimensional object angular or spatial frequency ranges.

28. A device for generating a microscope image of an object using Fourier holography, the device comprising: a radiation source for illuminating an object; an optical system for generating a Fourier hologram of the object, the optical system being arranged so that optical conditions can be changed in a manner such that Fourier holograms associated with respective object angular or spatial frequency ranges can be generated; a recording medium for recording the Fourier holograms, the recording medium being positioned on an optical axis of the device; and computer software for processing the recorded Fourier holograms in a manner such that the microscope image of the object is generated from a combination of Fourier holograms associated with respective object angular or spatial frequency ranges.