Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
  • G01J3/28—Investigating the spectrum
  • G01J3/2846—Investigating the spectrum using modulation grid; Grid spectrometers
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
  • G01J3/02—Details
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
  • G01J3/02—Details
  • G01J3/0205—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
  • G01J3/02—Details
  • G01J3/0205—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows
  • G01J3/0208—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows using focussing or collimating elements, e.g. lenses or mirrors; performing aberration correction
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
  • G01J3/02—Details
  • G01J3/0205—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows
  • G01J3/0218—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows using optical fibers
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
  • G01J3/02—Details
  • G01J3/0205—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows
  • G01J3/0229—Optical elements not provided otherwise, e.g. optical manifolds, diffusers, windows using masks, aperture plates, spatial light modulators or spatial filters, e.g. reflective filters

Definitions

• Embodiments of the present invention relate to aperture-coded spectroscopy.
• embodiments of the present invention relate to systems and methods for estimating the mean spectral density of a diffuse source in a single time step of parallel measurements using a static multimode multiplex spectrometer.
• a diffuse source is a source that inherently produces a highly spatially- multimodal optical field. In simplest terms, this is a spatially-extended source with an angularly-extended radiation pattern. The constant radiance theorem complicates the characterization of such sources. In short, entropic considerations require that the modal volume of a source cannot be reduced without a concomitant reduction in power. As a result, the brightness of diffuse sources . cannot be increased.
• the throughput of an optical instrument can be approximated as the product of the area of the input aperture and the solid angle from which the instrument will accept light.
• the acceptance solid angle is determined by the internal optics of an instrument.
• the only way to increase the etendue of the system is to increase the size of the input aperture.
• such an approach reduces the resolution of the spectrometer as it increases the throughput.
• a design that solves the first problem is said to have a Jacquinot (or large-area or throughput) advantage.
• a design that solves the second problem is said to have a Fellgett (or multiplex) advantage.
• a coded aperture or mask is used to convert intensity information into frequency or spectral information.
• the basic elements of a coded aperture imaging spectrometer are described in Mende and Claflin, U.S. Pat. No. 5,627,639 (the '639 patent), for example.
• Light from multiple locations on a target is incident on a mask.
• the mask contains rows and columns of both transmissive and opaque elements.
• the transmissive and opaque elements are located on the mask according to a transfer function used to convert intensity information of the incident light to spectral information.
• the transmissive elements transmit the incident light, and the opaque elements block the incident light.
• a grating is used to disperse the transmitted light from the.
• transmissive elements in a linear spatial relationship, according to the wavelength of the transmitted light.
• the dispersed light is incident on a detector array.
• the detector array contains rows and columns of detector elements.
• the detector array elements are designed to receive a different range of wavelengths from each transmissive element of the mask and provide a signal indicative the intensity of the light received.
• the mask is translated in one direction relative to the target over time.
• a data matrix is generated.
• the data matrix contains light intensity data from each row of the detector array as light incident from the same target elements passes through a corresponding row of the mask.
• the intensities recorded by the rows and columns of detector elements are collected over time and assembled in a data matrix for each set of target elements.
• a frequency spectrum is obtained for each set of target elements by converting the data matrix according to the transfer function.
• a pattern matrix is predetermined from the mathematical representation of the mask elements.
• Transmissive elements of the mask are represented as a '1' in the pattern mask, and opaque elements of the mask are represented as a '0' in the pattern mask.
• a frequency matrix representing the frequency spectrum is obtained by multiplying the data matrix by the inverse pattern matrix and a factor that is a function of the number of transmissive elements and number of total mask elements.
• Coded aperture spectroscopy was proposed in Golay, M. J. E. (1951), "Static multislit spectrometry and . its application to the panoramic display of infrared spectra.” Journal of the Optical Society of America 41(7): 468-472. Two- dimensional coded apertures for spectroscopy were developed in the late 1950's and early 1960's as described, for example, in Girard, A. (1960), "Nouveaux gebers de spectroscopie a grande luminosite,” Optica Acta 7(1): 81 - 97.
• coded aperture spectroscopy instruments were limited to single optical detector elements or small arrays of discrete detectors. Reliance on single detectors required mechanical, electro-optical, liquid crystal, or other forms of modulation to read spectral data. These early coded aperture instruments implemented spectral processing by using both an entrance and an exit coded aperture and a single detector element or a detector element pair.
• Aperture coding is not the only approach to solving these spectrometer design problems.
• Interferometric spectrometers such as Fourier transform (FT) spectrometers, can also exhibit the Jacquinot and Fellgett advantages.
• the FT spectrometer in fact exhibits both.
• the majority of FT spectrometers contain mechanical scanning elements.
• a class of aperture coded spectrometer is optimized for the spectral characterization of diffuse sources.
• the spectrometer achieves high throughput and high spatial resolution by replacing the slit of conventional dispersive spectrometers with a spatial filter or mask.
• a number of masks can be used including Harmonic masks, Legendre masks, and Hadamard masks.
• the present invention is a static multimode multiplex spectrometer (MMS).
• MMS includes a two-dimensional orthogonal column code mask, wherein source radiation is incident on the mask, wherein the transmissive and opaque elements of the mask are arranged according to a transfer function represented mathematically as a coding matrix, and wherein each column of the coding matrix is orthogonal under an inner product transformation.
• the MMS further includes a dispersive element aligned with the code mask, wherein source radiation transmitted through the mask is incident on the dispersive element such that the dispersive element induces a wavelength dependent spatial shift of the image of the mask.
• the MMS further includes a two-dimensional detector array aligned with the dispersive element, wherein source radiation from the dispersive element is incident on the array, wherein the array comprises row and column detector elements, and wherein the detector elements convert the wavelength dependent spatial shift image of the mask into a light intensity values.
• the MMS also includes a processing unit, wherein the processing unit stores the values in a data matrix and performs a transformation of the data matrix using the coding matrix to produce a spectrum matrix that is a mathematical representation of a spectral density of the source radiation.
• Figure 1 is a schematic diagram of an exemplary multimode multiplex spectroscopy system, in accordance with an embodiment of the present invention.
• Figure 2 illustrates a coordinate system used to describe embodiments of the present invention.
• Figure 3 is an exemplary aperture pattern for an independent column code based on harmonic functions according to an embodiment of the present invention.
• Figure 4 is an exemplary aperture pattern for an independent column code based on Legendre polynomials according to an embodiment of the present invention.
• Figure 5 is an exemplary aperture pattern for an independent column code based on a Hadamard matrix according to an embodiment of the present invention.
• Figure 6 is an exemplary aperture pattern for an orthogonal column code (in conjunction with processing of the measured intensity) based on a row-double
• Figure 7 is an exemplary raw image captured at the focal plane illustrating smile distortion.
• Figure 8 is an exemplary charge coupled device image showing uncorrected spectral line curvature as a function of vertical field position, in accordance with an embodiment of the present invention.
• Figure 9 is an exemplary charge coupled device image showing corrected spectral line curvature as a function of vertical field position, in accordance with an embodiment of the present invention.
• Figure 10 is an exemplary plot of reconstructed spectrum with horizontal nonlinearity correction and reconstructed spectrum without horizontal nonlinearity correction, in accordance with an embodiment of the present invention.
• Figure 11 is a graphical comparison of results from a reconstructed spectrum from a mask based on H 40 and a slit aperture.
• Figure 12 is a graphical comparison of results from reconstructed spectra from row-doubled Hadamard masks of various orders.
• Figure 13 illustrates throughput gain achieved by order-N masks compared to slits of equivalent height.
• Figures 14a and 14b is a graphical comparison of a small spectral peak as reconstructed by a mask based on H 40 and a slit aperture.
• Figure 15 is a schematic diagram showing an exemplary system for converting a spatially non-uniform source of interest to a spatially uniform source of interest using a Fourier-transform lens, in accordance with an embodiment of the present invention.
• Figure 16 is a schematic diagram showing an exemplary system for converting a spatially non-uniform source of interest to a spatially uniform source of interest using a ground-glass diffuser, in accordance with an embodiment of the present invention.
• Figure 17 is a schematic diagram showing an exemplary system for converting a spatially non-uniform source of interest to a spatially uniform source of interest using a multimode fiber bundle, in accordance with an embodiment of the present invention.
• Figure 18 is a schematic diagram showing an exemplary system for astigmatic imaging and intensity field homogenization using astigmatic optics, in accordance with an embodiment of the present invention.
• Embodiments of systems and methods relate to a two-dimensional orthogonal column code multimodal spectrometer and spectral imager are described in this detailed description of the invention, which includes the accompanying Appendix 1 of the '522 application and Appendix 1 of the '173 application.
• Appendix 1 of the '522 application and Appendix 1 of the '173 application.
• numerous specific details are set forth to provide a thorough understanding of embodiments of the present invention.
• One skilled in the art will appreciate, however, that embodiments of the present invention may be practiced without these specific details.
• structures and devices are shown in block diagram form.
• Embodiments of the present invention provide a static two-dimensional aperture coding for multimodal multiplex spectroscopy. Below, a mathematical model of a dispersive spectrometer is derived, and it is shown how simple aperture codes can result in both Jacquinot and Fellgett advantages. Several different classes of aperture patterns are described. In addition, experimental results from static multimodal multiplex spectroscopy are presented.
• a primary goal of a static multimode multiplex spectrometer is to estimate the mean spectral density S (X) of a diffuse (multimodal) source.
• S (X) mean spectral density of a diffuse (multimodal) source.
• Static refers to the lack of mechanical, electro-optical or other active modulation in forming the source estimate.
• a preferred static MMS estimates S (X) in a single time step of parallel measurements.
• a preferred MMS system measures spectral projections of the field drawn from diverse modes or points and combines these projections to produce an estimate of the mean spectral density.
• FIG. 1 is a schematic diagram of an exemplary MMS system 100, in accordance with an embodiment of the present invention.
• System 100 is a grating spectrometer with a two-dimensional coded aperture mask 110 taking the place of the entrance slit of a conventional system. Unlike many previous coded aperture spectrometers, system 100 does not use an output slit. The output aperture is fully occupied by a two-dimensional optical detector array 120.
• System 100 images aperture coding mask 110 onto optical detector array 120, through a dispersive element 130.
• Aperture coding mask 110 preferably contains aperture codes and weighting on the aperture codes such that each column of the pattern or coding matrix is orthogonal under an inner product transformation.
• Optical detector array 120 is a two-dimensional charge coupled device (CCD), for example.
• Dispersive element 130 can include but is not limited to a grating, a holographic grating, or a prism. Dispersive element 130 can include a combination of dispersive elements. Dispersive element 130 induces a wavelength dependent spatial shift of the image of aperture coding mask 110 on detector array 120.
• System 100 preferably includes a relay optical system 140.
• Relay optical system 140 is used to convert a non-uniform spectral density of source radiation
• System 100 also preferably includes an imaging lens system 160 and an imaging lens system 170.
• the combined imaging system 160 and 170 is designed to form an image of the aperture mask 110 on the focal plane 120 through the grating 130 such that the image position shifts linearly as a function of illumination wavelength.
• I(x', y') y)(T(x, y)S(x, y, ⁇ ) (12)
• H(x,y) is the kernel describing propagation through the spectrometer
• T( x, y) is a transmission function describing the input aperture
• S(x,y, ⁇ ) is the input spectral density at position (x, y).
• unprimed variables denote quantities defined in the input plane
• primed variables denote quantities in the detector plane.
• a propagation kernel for a dispersive spectrometer according to an embodiment of the present invention may be modeled as
• Eqn. (14) reveals that the intensity profile in the detector plane is a direct estimate of the spectral density at the slit location.
• the drawback to such an approach is that the throughput of the system is severely curtailed. More complicated aperture patterns, however, can increase the photon collection efficiency of the system.
• a goal of the MMS is to develop an apert ⁇ re code that permits estimation of the mean spectrum across an extended aperture.
• the mean spectrum across an extended aperture is defined as:
• Eqn. (20) can be interpreted as a two-dimensional function containing estimates of the input spectrum at different input locations. A slice through this function at a constant value of x" corresponds to the input spectrum at a particular value of x. In other words, at this point, a ID imaging spectrometer, has been created. Conversion of E(x', x") into an estimate of S mean ( ⁇ ) is described below.
• Eqn. (19) can be written in a form where x and x" are parameters rather than coordinates.
• Eqn. (22) is identical to the orthogonality constraint for eigenfunctions in Sturm-Liouville theory, with I(y) acting as the weighting function and p acting as the norm. Therefore, the design requirement of Eqn. (19) can be met by basing the input aperture pattern on any family of orthogonal functions.
• T and f are not the same set of codes, the system is said to be non-self- adjoint.
• complete set of codes in T can be viewed as abstract vectors defining a non-orthogonal basis on a Hubert space.
• Such a family of codes is referred to as an independent column code.
• x and x can be either continuous or discrete parameters depending on the eigenvalue spectrum of the chosen family of functions. In the discrete case, the Dirac delta function ⁇ (x - x”) is properly replaced with the
• the light falling at a given value of x' in the detector plane arises from a combination of different wavelengths passing through different locations on the input aperture.
• a well-designed code allows breaking this ambiguity and determining the spectral content of the light.
• the intensity profile I(y) was shown to act as a weighting function in
• the codes have been chosen such that the transmission has physically-realizable values in the interval [0,1].
• the exemplary pattern illustrated in Fig. 4 is continuous vertically, but discrete horizontally. [0069]
• continuous functions of y have been considered as possible code families. Based on the heuristic insights described above in paragraph [0060], it seems reasonable to also consider discontinuous functions that are pixelated in the y direction. A choice, for example, are pixelated functions based on Hadamard matrices.
• H n an order-n Hadamard matrix
• H n (:, m) and H n (m, :) refer to the mth column and row of Hn, respectively.
• r x ,7> e ⁇ H n (:,m) ⁇ m ⁇ n (33) is a self-adjoint set of codes.
• the elements of a Hadamard matrix are either 1 or - 1 , this is again not realizable with incoherent illumination. Shifting and scaling the code values results in a non-self- adjoint independent column code
• any row of the code contains both positive and negative values.
• the multiplex nature of the system then ensures that light from these different regions are combined on the detector plane, making it impossible to apply the appropriate weighting in software.
• positive and negative regions of the code can be segregated onto separate rows. A weighting could then be applied to entire rows in the detector plane and to achieve the desired effect.
• each original row H n (m, : . ) is replaced with two rows:
• H n If a row-doubled version of H n as denoted H n , then
• Fig. 6 An aperture based on a row-doubled Hadamard matrix is shown in Fig. 6. The codes have been chosen such that the transmission has physically-realizable values in the interval [0,1].
• the exemplary pattern illustrated in Fig. 6 is discrete both horizontally and vertically.
• the aperture must be designed so that when imaged onto the detector, the features involve integral numbers of pixels in the y' direction. This places performance requirements on the manufacturing accuracy of the aperture and the magnification of the relay optics in the spectrometer.
• an aperture involving a discrete code must be aligned with respect to the detector plane such that the divisions between features align with divisions between pixels. This requires sub-pixel positioning ability on the input aperture during construction and alignment.
• One alternative is to convert the designed continuous-tone mask into a half -toned version. A small region of the continuous-tone pattern is subdivided into an array of even smaller subregions. Each of these subregions is assigned a transmission of either 0 or 100%, such that the net transmission in the region matches the grayscale value of the continuous-tone pattern. Provided that the conversion happens on a spatial scale that is smaller than the pixelization of the detector plane, no significant difference should be detectable.
• the internal optics of the spectrometer can have a significant effect on the performance of the system.
• the optical properties of a static MMS deviate from a traditional instrument in a critical manner. Because the MMS encodes spectral information across the detector plane in a highly non-local way, optical errors anywhere have a non-local effect on the reconstruction, introducing noise and errors at regions throughout the spectral range.
• H(x, y) S(y - y') ⁇ (x - (x f + a ⁇ + ⁇ c )).
• the spectral resolution of the instrument should be limited by the width of a feature on the input mask Ax. This requires that the size of the incoherent impulse response be small compared to Ax. Further, the size of the impulse response should not vary significantly across the input and output fields.
• the impulse responses in the x and y directions should be uncorrelated. This requires that the optical system have low distortion across the input and output fields. 3.
• the input intensity profile should be unaffected by propagation through the system (aside from a wavelength-dependent shift in x direction. This requires that there be no field-dependent intensity modulations (vignetting) in the system. [0084]
• the ideal imaging kernel can break down in another way as well.
• Digital compensation techniques can be used to correct for the spectrum line curvature and the nonlinear dispersion of the spectra onto the detector array prior to spectral estimation.
• a calibration source with narrow peaks such as a gas discharge lamp, calibration parameters can be stored and used on further data sets.
• Figure 8 is an exemplary CCD image 800 showing uncorrected spectral line curvature as a function of vertical field position, in accordance with an embodiment of the present invention.
• the linear displacement from a straight image, A ⁇ can be described by where ⁇ is the vertical angle of the ray hitting the grating, ⁇ is the wavelength of the light, and A is the angular dispersion of the grating for a nonzero ⁇ .
• the CCD image is first interpolated to a higher resolution horizontally using a cubic spline function.
• a vector is then formed of column positions of vertical features of the mask and a vector of the corresponding rows is formed as well.
• a polynomial fit is then used to find a relationship between the linear displacement and the CCD row. For narrow wavelength ranges, the same correction can be used for all the columns of the CCD. If broader wavelength ranges or higher resolution corrections are required, then mask features from multiple spectral lines have to be used, and the correction is dependent on the CCD column as well.
• Figure 9 is an exemplary CCD image 900 showing corrected spectral line curvature as a function of vertical field position, in accordance with an embodiment of the present invention.
• a digital correction technique is used that involves averaging the multiple spectral estimates. After the inversion of the formatted CCD data, spectral estimates at the different slit positions are determined.
• a reconstructed data set from a calibration source such as a pen lamp is also used.
• Vectors are then formed of the pixel positions of the strongest peaks in the spectra for each spectral estimate.
• Vectors are then formed of the required pixel positions in order to keep the spacing of the peaks the same in each estimate, since the source spectra line positions are fixed.
• a polynomial fit is performed to relate the column of the CCD and its deviation from these required pixel positions.
• the reconstructed spectra are then resampled using this polynomial fit onto a corrected axis.
• the spectra are aligned and summed in order to form a spectral estimate.
• Figure 10 is a plot 1000 exemplary of reconstructed spectrum with horizontal nonlinearity correction 1010 and reconstructed spectrum without horizontal nonlinearity correction 1020, in accordance with an embodiment of the present invention.
• plot 1000 the width of the far peak is decreased and its height increased after the correction is performed.
• the calibration data for both corrections are stored, and are used for every future reconstruction involving arbitrary sources.
• the spectral source was a xenon discharge lamp operated in conjunction with an integrating sphere.
• the light from the integrating sphere was allowed to fall directly on the mask aperture no relay optics of any kind were used.
• the CCD integration time was 160 ins.
• the particular spectrometer has a spectral range of ⁇ 775 - 900 nm.
• the spectral resolution depends on the mask used. For the majority of the masks, the resolution is ⁇ ⁇ 0.65 nm.
• the masks consisted of chrome deposited on a quartz substrate. The smallest mask feature was 36 gm, corresponding to 4 pixels on the CCD.
• Fig. 11 compares the spectrum reconstructed from an order-40, row-doubled
• Fig. 13 illustrates that the observed scaling is approximately N/4, rather than the expected N/2.
• MTF modulation transfer function
• Figs. 14a and 14b shows a region of the xenon spectrum containing a very small peak (so weak that it is not visible at the scales of the previous figures).
• Fig. 14a shows the peak as reconstructed by the row-doubled, order-40 Hadamard mask. The bottom plot is the peak as measured by the slit aperture. If the SNR of the peak is defined to be its height divided by the rms value of the region near the peak, we find that the SNR for the mask aperture is ⁇ 23.7 while the SNR for the slit is ⁇ 7.0.
• the source of interest is spatially non-uniform.
• a source of interest that is spatially non-uniform is modeled by assuming that the input spectral density is S (JC, y,X) ⁇
• Spectral analysis with orthogonal column codes requires that the spectral density be uniform or approximately uniform with respect to y .
• Figure 15 is a schematic diagram showing an exemplary system 1500 for converting spatially non-uniform source of interest to a spatially uniform source of interest using a Fourier-transform lens 1510, in accordance with an embodiment of the present invention. If the source radiation is spatially incoherent in an input plane 1520, placing Fourier-transform lens 1510 between input plane 1520 and a mask plane 1530 produces a uniform illumination. Fourier-transform lens 1510 is situated one focal length from source input plane 1520 and one focal length from coding mask plane 1530.
• Figure 16 is a schematic diagram showing an exemplary system 1600 for converting a spatially non-uniform source of interest to a spatially uniform source of interest using a ground-glass diffuser 1610, in accordance with an embodiment of the present invention. If the incoherence of a source cannot be guaranteed, placing a ground glass diffuser 1610 between input plane 1620 and mask plane 1630 produces a uniform illumination.
• Figure 17 is a schematic diagram showing an exemplary system 1700 for converting a spatially non-uniform source of interest to a spatially uniform source of interest using a multimode fiber bundle 1710, in accordance with an embodiment of the present invention. Similarly, if the incoherence of a source cannot be guaranteed, placing multimode fiber bundle 1710 between input plane 1620 and mask plane 1630 produces a uniform illumination.
• the spectral density in the coded mask plane may be assumed to be
• FIG. 18 is a schematic diagram showing an exemplary system 1800 for astigmatic imaging and intensity field homogenization using astigmatic optics, in accordance with an embodiment of the present invention. Spatial uniformity in the y direction and imaging in the x direction may be achieved using astigmatic optics such that the y direction focal length is twice the x direction focal length.
• placing cylindrical Fourier-transform lens 1810 and cylindrical imaging lens 1820 between input plane 1520 and mask plane 1830 produces a uniform intensity field in the y direction, but retains variation in the x direction.
• the spectral density on coded mask plane 1830 is
• the signal from the detector array is a
• Figures 19-23 illustrate image rotation in the input aperture of system
• instructions adapted to be executed by a processor to perform a method are stored on a computer-readable medium.
• the computer-readable medium can be a device that stores digital information.
• a computer-readable medium includes a read-only memory (e.g., a Compact Disc-ROM ("CD-ROM”) as is known in the art for storing software.
• CD-ROM Compact Disc-ROM
• the computer-readable medium can be accessed by a processor suitable for executing instructions adapted to be executed.
• instructions configured to be executed and “instructions to be executed” are meant to encompass any instructions that are ready to be executed in their present form (e.g., machine code) by a processor, or require further manipulation (e.g., compilation, decryption, or provided with an access code, etc.) to be ready to be executed by a processor.
• Coupled encompasses a direct connection, an indirect connection, or a combination thereof.
• Two devices that are coupled can engage in direct communications, in indirect communications, or a combination thereof.
• two devices that are coupled need not be in continuous communication, but can be in communication typically, periodically, intermittently, sporadically, occasionally, and so on.
• communication is not limited to direct communication, but also includes indirect communication.
• Systems and methods in accordance with an embodiment of the present invention disclosed herein can advantageously maximize spectrometer throughput without sacrificing spectral resolution and maximize the signal-to-noise ratio of an estimated spectrum for a given system throughput and detector noise.

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