Optical Scatter Imaging with a Digital Micromirror Device References and Links

We had developed Optical Scatter Imaging (OSI) as a method which combines light scattering spectroscopy with microscopic imaging to probe local particle size in situ. Using a variable diameter iris as a Fourier spatial filter, the technique consisted of collecting images that encoded the intensity ratio of wide-to-narrow angle scatter at each pixel in the full field of view. In this paper, we replace the variable diameter Fourier filter with a digital micromirror device (DMD) to extend our assessment of morphology to the characterization of particle shape and orientation. We describe our setup in detail and demonstrate how to eliminate aberrations associated with the placement of the DMD in a conjugate Fourier plane of our microscopic imaging system. Using bacteria and polystyrene spheres, we show how this system can be used to assess particle aspect ratio even when imaged at low resolution. We also show the feasibility of detecting alterations in organelle aspect ratio in situ within living cells. This improved OSI system could be further developed to automate morphological quantification and sorting of non-spherical particles in situ. Calcium-induced alterations in mitochondrial morphology quantified in situ with optical scatter imaging, " Biophys. The C-terminal transmembrane domain of Bcl-xL mediates changes in mitochondrial morphology, " Biophys.(L)-dependent light scattering by apoptotic cells, " Biophys. Confocal pattern period in multiple-aperture confocal imaging systems with coherent illumination, " Opt. An optical sectioning programmable array microscope implemented with a digital micromirror device, " J. High-speed addressable confocal microscopy for functional imaging of cellular activity, " J. Automated digital light modulation microscope (DLMM) for living cell array analysis: pattern recognition and spatial alignment, " in Fiber-optic confocal microscopy using a spatial light modulator, " Opt. Quantitation and mapping of tissue optical properties using modulated imaging, " J. Index-of-refraction-dependent subcellular light scattering observed with organelle-specific dyes, " J.


Introduction
Alterations in the morphology of subcellular organelles are an important indicator of cellular function.To facilitate detection and tracking of subcellular morphology changes, we had developed an optical scatter imaging (OSI) technique that consisted of measuring the intensity ratio of wide-to-narrow angle scatter to assess subcellular particle size within living cells [1].In a transmission microscope utilizing the central dark-ground method, wide and narrow angles of scatter were selected by varying the diameter of a circular iris in a Fourier plane, conjugate to the objective's back focal plane.
Using this method, we showed that changes in subcellular scattering can be correlated with mitochondria-specific treatments such as cyclosporine-A-dependent calcium injury [2] or altered expression of Bcl-2 family proteins which specifically target the mitochondrial outer membrane [3].Subcellular optical scatter changes were also induced by apoptosis in a Bcl-x L dependent manner [4].Nonetheless, one of the limitations of this previous method is that despite being sensitive to changes in particle shape and size, it could not distinguish between them.Thus, to quantify the shape of non-spherical organelles, such as mitochondria, and the anisotropic morphological changes that characterize their activity, we extended the previous OSI method by replacing our variable diameter iris with a digital micromirror device (DMD) as a Fourier filter [5].
In a microscopy system, the DMD is often used in a conjugate image plane as an adjustable, dynamic aperture that can increase spatial resolution, gain flexibility, or facilitate quantitative analysis.For instance, a DMD could be used to replace simple microscopy diaphragms to allow more flexible control of sample illumination and light detection [6,7].A DMD was incorporated into programmable array microscopes to replace the conventional Nipkow disc and achieve multiple-aperture confocal imaging [8,9].A high-speed addressable confocal microscope was built by combing an acousto-optic deflector with a DMD for point illumination and point detection [10].A DMD could be used for modulation of excitation light in dynamic cell screening [11], for sequential fiber illumination and sample scanning in confocal endo-microscopy [12], and for digital fringe projection combined with phaseshifting to provide microscopic 3-D shape measurement [13] or controlled optical sectioning in a fullfield fluorescence microscope [14].Modulated imaging utilizing projection of sinusoidal illumination patterns using a DMD was also used for quantification and mapping of optical properties in turbid tissue [15].
In contrast with these microscopy applications, we use our DMD in a conjugate Fourier plane.This results in convolving the DMD transform with the object field function as opposed to multiplying the DMD pattern with the object field function when the DMD is used in a conjugate image plane.The main purpose of this paper is to describe our instrumentation in detail, to discuss the image artifacts resulting from positioning the DMD in the Fourier plane, and to show how these artifacts may be overcome.We also show pilot data from bacteria and spheres, as well as cells to demonstrate the potential ability of our DMD-based optical scatter imaging approach to differentiate particles based on their aspect ratio.

Microscope Setup
The DMD based optical scatter imaging setup is shown in Fig. 1.Narrow-band laser light from a ~5 mW Helium-Neon laser (Research Electro-optics, Boulder, CO, line at λ o = 632.8nm) was passed through a ground glass diffuser (DG20-120, Thor Labs, NJ) spinning at > 1,000 rpm.The diffused light was collected by an aspheric lens (C330TM-A, Thorlabs, NJ) with 3.10mm focal length and 0.68NA, collimated by an f=25.4mmlens and coupled into a multimode fiber (F-MLD-C-5FC, NA=0.29 Newport, Irvine, CA) by an aspheric fiber collimation package (Thorlabs F220FC-B, f = 11 mm, NA=0.25).The fiber output was collimated using an f = 15.3 mm, NA = 0.16 aspheric lens (F260FC-A, Thorlabs, NJ) and launched into the condenser of an inverted microscope (Zeiss, Axiovert 200M, Göttingen, Germany) aligned in central Köhler illumination (NA<0.05) to provide a spatially coherent plane wave.The microscope was fitted with a 20x dry objective (NA=0.75).The DMD (TI 0.7 XGA DMD, Texas Instruments) was placed in a conjugate Fourier plane, F" in Fig. 1, outside the microscope side port.The DMD consists of a 1024×768 array of aluminum micromirrors, 13.68×13.68µm 2 , each mirror operates in a bistable mode, tilted diagonally + 12° or −12° [16,17].Four lenses, L1-L4 were used to control the magnification of the image transform on the DMD, to collimate the imaging beam (red beam) on the DMD, and to focus the specimen's image on the CCD camera (Cascade 512B, Roper Scientific).It was important to collimate the imaging beam on the DMD to avoid geometric aberrations originating from reflection by the array of tilted DMD mirrors.In this condition, the array of tilted mirrors will cause a linear phase shift as a function of mirror position.This results in shifting the final image without distortions as long as the angle of incidence on the DMD and the tilt angle of the mirrors are small.The camera was placed on a rail positioned at an angle of 24° with respect to the microscope's side port axis to collect scattered light reflected by the DMD mirrors tilted + 12° ("on" mirrors).Scattered light reflected by mirrors tilted −12° ("off" mirrors) was directed away from the CCD and blocked.Image acquisition consisted of collecting on the CCD a stack of spatially filtered dark-field images using a spatial filter bank generated by the DMD.A beam block consisting of a 0.3mm graphite pencil lead glued to a No. 1 cover slip was centered in F' (Fig. 1) to minimize the dark-field background (See Results).
The measured efficiency of our DMD was ~45% by taking the ratio of the light intensity reflected by the DMD to the light intensity incident on the DMD.This value which takes into account the DMD's fill factor, diffraction efficiency, mirror reflectivity and window transmittance, is lower than the value of 68% reported in the manual specifications.This is likely due to the fact that the DMD blaze wavelength is 656nm for 0° incidence.Thus, using a laser source with a wavelength closer to 656nm or varying the angle of incidence by about a degree could improve throughput.

Generation of DMD filters
Binary images in Bitmap format were loaded onto the DMD via the DMD Discovery 1100 control software (Texas Instruments).This graphical user interface allows us to directly select a bitmap image file and load it onto the DMD via a USB 2.0 interface, without needing to display the file on a full computer screen or use the DMD as a secondary computer monitor display.Bitmap images containing 768x1024 pixels with values of 0 or 1 were generated to match the position of the mirrors in the DMD array.The DMD was oriented such that a pixel value of zero results in turning on the corresponding mirror to reflect the light falling on it towards the CCD, while a pixel value of 1 corresponds to turning off the mirror and deflecting the light away from the CCD.If images are being continuously cycled at 150fps, then the DMD receives reset pulses between cycles (off duty).However, if an image is displayed for an extended time period on the DMD, an automatic reset will take place every ~1-2s to avoid unstuck mirrors.For the TI 0.7 XGA DMD used in this paper, the reset function affects both the On and the Off mirrors and consists of reset pulses of 24µs duration during which the mirrors receive a small pulse that causes a small wobble of the mirrors without completely rotating them by 24°.In our setup, we assumed that the increase in background due to these reset pulses is smaller than, or on the order of, the background level obtained by blocking unwanted signal while the mirrors are switched off.Thus, the change in signal-to-noise ratio due to the reset pulses was neglected.
Using the diffraction pattern of a graticule with line spacing b=10µm, we converted mirror positions on the DMD to spatial frequency in cycles/µm.For the graticule, each order of diffraction collected by the objective falls at an angle, θ, with respect to the optical axis.The spatial frequency was defined as sinθ/λ ο = m/b; m is the order number.The positions of the diffraction orders were measured in mirrors from the zeroth order position (zero frequency component at the center of the DMD) in the Fourier plane with the aid of a mirror ruler consisting of DMD passbands at regular intervals and plotted against diffraction order number (or spatial frequency).A linear fit to the measurements gave 12.55 mirrors per diffraction order, or 0.00797 cycles/µm/mirror and a correlation coefficient of 0.99.The maximum aperture (NA= 0.75) corresponds to NA/λ o = 1.185 cycles/µm or a radius of 149 DMD mirrors.The microscope aperture was not projected on the full width of the DMD to avoid image aberrations originating from the edges of the device (See Results).
We used the DMD to generate Gabor-like filters, which we described recently [5].In this report, a filter bank with frequency center, 1/S, at = 0.805 cycles/µm (mirror #101 from the DMD center) and spanning various orientations, 0°≤ φ< 180° in Fourier space, with 10° increments, was used to infer particle roundness and aspect ratio.As in [5], we approximated each Gaussian shaped filter by generating four binary concentric discs and summing their corresponding filtered images.This results in adding four intensity images instead of filtering both the phase and amplitude of the E-field in the Fourier plane, but provides a good approximation since the phases of the resulting four images are not significantly different due to the co-localization of the concentric disks in the Fourier plane.As in [5], we designed the filters so that the standard deviation of the Gabor Gaussian envelope was σ=S/2, which gives 1/(2*0.805)=0.621µm in the present paper.

Sample preparation
Immobilized spheres and E. coli samples Samples of stationary particles consisting of polystyrene spheres (Polysciences, Warrington, PA, diameter = 0.465 µm or 0.494 µm) and fixed E. coli bacteria were used in this study to demonstrate the feasibility of quantifying particle asymmetry with the DMD-based optical scatter imaging setup.The 0.494 µm microspheres are labeled with three different fluorescent dyes with excitation maxima of 377, 517 and 588nm, and emission maxima of 479, 546 and 612nm, respectively.E. coli were first fixed with 2% paraformaldehyde for 15 minutes followed by three washes in phosphate buffered saline (PBS) and stored in water at 4°C.Spheres and E.coli were either used alone or mixed together and were embedded in 2.5% arcrylamide gel.The final concentration of E. coli in acrylamide was around 6.5×10 8 cells/mL, and the final concentration of spheres corresponded to a scattering coefficient, µ s, = 0.0025 µm −1 .A 3µL aliquot was placed between a microscope slide and a 22mm x 22mm coverslip and allowed to gel thus immobilizing the particles within the sample.The thickness of the gel was 5.2 µm.Samples were prepared at very low concentration so that particles were separated from each other and individual particles could be observed.

Living cells
Immortalized baby mouse kidney (iBMK) cells were maintained in Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% (V:V) fetal bovine serum (FBS), 100 Units/ml penicillin, and 100 µg/ml streptomycin.FBS was from Gemini Bio-Products, DMEM, penicillin, streptomycin were from Invitrogen.The cells were kept in culture at 38°C in an 8.5% CO 2 in air atmosphere.Twenty four hours before imaging, the cells were cultured on glass coverslips to allow attachment.Before transferring to the microscopy stage, cells were incubated for 30 minutes in growth medium supplemented with 50nM Mitotracker Green (Invitrogen) to visualize specifically the mitochondria.Coverslips were then mounted on a steel plate and the growth medium was replaced with Leibovitz's L-15 medium (Invitrogen) supplemented with 10% FBS, 100 Units/ml penicillin, and 100 µg/ml streptomycin.

Requirement for narrow-band light source to avoid chromatic aberrations
Due to the tilt of the DMD mirrors during on/off actuation, the desired image of the object is projected at the specular reflection angle relative to the DMD mirrors.Thus, when placed in a conjugate Fourier plane, the DMD mirrors act like a blazed grating, and the desired image is found in the sixth order of diffraction by the DMD rather than the zeroth order (m=6 for wavelength λ blaze = 655.5nm).The DMD mirrors are 13.68µm x 13.68µm and tilt around their diagonal at 45°.Thus, if the microscope aperture were projected on the full width of the DMD, which has 768 mirrors, this grating would have N=1536 lines with 9.67µm separation and its resolution would be λ ο /∆λ= mN= 9216 with ∆λ=0.069nmaround 633nm.Thus, a source bandwidth ∆λ>0.07nm will create a significant chromatic aberration consisting of smearing a point source object in the direction of the mirror tilt (the extent of the smear scales with the source bandwidth).An example is shown for a filtered halogen source with λ o = 633 ± 0.5 nm (Fig. 2a and 2c).This problem was resolved with the use of a narrow band laser source, such as the Helium Neon laser used here with ∆λ=0.0006nm (Fig. 2b and 2d).As can be seen in Fig. 2d, the current resolution of the system when operating in unfiltered dark-field is 0.675µm (full width at half maximum of the point spread function is ~2.5 pixels with 0.27µm/pixel).This resolution compares well with the 0.515µm diffraction limit of resolution expected from our 0.75 NA objective using the Rayleigh criterion for distinguishing two point sources.Increasing the magnification would have allowed us to better sample the pointspread-function with more than two pixels.However, in our application, the resolution element of our filtered images is ultimately given by the extent of the Gabor filters in image space and is proportional to the standard deviation of the filter's Gaussian envelope, σ, given in Section 2.2 (see also [5]).

DMD generated geometric aberrations
To maximize spatial frequency resolution, the object transform should be magnified to fill the full 768-mirror diameter of the DMD.However, when this is the case, we obtained image aberrations (Fig. 3a), which worsen as a point source object is moved in and out of focus, despite precise alignment of the optics in the setup.The DMD possesses a band of 6-8 mirrors at the edge of its active surface.This "pond of mirrors" is always in the binary "0" position.For the DMD orientation chosen here, a binary value of "0" corresponds to the "on" position and deflects the light towards the CCD.To investigate whether this rectangle of inactive mirrors gave rise to the aberrations shown in Fig. 3a, we rotated the DMD by 180° such that the rectangle of inactive mirrors with binary value of "0" was in the "off" position.However, this did not eliminate the aberrations (data not shown).These geometric aberrations were ultimately eliminated by reducing the size of the illumination beam to occupy a diameter of less than 400 mirrors at the center of the device (Fig. 3b).We also found that if the reflected beam covers less than 400 mirrors but is placed near one of the DMD edges, aberrations appear again suggesting that the edge of the device rather than the area of the DMD aperture is responsible for this effect (Fig. 3c).For the data shown in Fig. 3c, the whole DMD device was translated so that the center of the shifted active aperture was aligned with the incident beam.Thus, the beam reflected from the DMD's active aperture in (c) still passed through the center of L4 without vignetting.The source of the aberrations in Fig. 3 has not been fully elucidated, and in this paper, we limit ourselves to presenting our fix, which consist of using the central DMD mirrors.However, during our investigations we have also been able to rule out the following: 1) other optics in the setup do not contribute to the aberration, as simply replacing the DMD by a flat aluminum coated mirror rotated by 12° to reflect the light towards the camera succeeded to eliminate the aberration (data not shown); 2) the aberrations were not due to the tilt of the DMD mirrors.Actuating the DMD mirrors to "float" mode (all mirrors kept flat) and rotating the whole device by 12° to reflect the light onto the CCD gave the same aberration (data not shown);

Elimination of multiple images
The final image collected by the system shown in Fig. 1 will contain multiple images of the object as the original image of the object becomes convolved with the pixels of the DMD.If the elements of the DMD device are too large compared to the width of the object transform, the desired image of the object will overlap with the images found in the adjacent diffraction orders.This effect is exacerbated by the fact that the transform was reduced to occupy less than the full area of the DMD (See Section 3.2).An image of the field of view shows the extent of this multiple image overlap (Fig. 4a).The additional images were deconvolved using a standard Wiener filter algorithm (Matlab's "deconvwnr" function).For this, three pixels were selected that were positioned on the same object feature, which appeared in the multiple images.These pixels were simultaneously shifted to let the point in the central image fall on the center of the image.The pixels were then weighted by their intensity in the original image.The image of the three centered and intensity weighted pixels (green pixels in Fig. 4a) consisted of the point spread function used for the deconvolution algorithm.The deconvolved image is shown in Fig. 4b.Figures 4c and 4d show pixel histograms of two pairs of adjacent regions with and without overlap, before (regions (a1,a2) and (a3,a4) in Fig. 4a) and after (regions (b1, b2) and (b3, b4) in Fig. 4b) deconvolution.After deconvolution, the intensity distribution of areas (b1,b2) and (b3,b4) become largely similar attesting to the success of the algorithm at eliminating the overlapping signal.The intensity of the peripheral images was at most 12% of the intensity in the central image.Thus the additional shot noise contributed by the additional background in the overlapping image regions is not significant.

Spinning diffuser to reduce speckles
To reduce the speckle effect due to imaging with the laser source, we placed a ground glass diffuser spinning at >1,000 RPM before coupling the laser into the optical fiber.Figure 5a shows the background imaged without the diffuser.The uniformity of the background in the whole image was 2261±1597 (mean ± standard deviation) counts/100ms, which had a 70% coefficient of variation (CV).Using the spinning diffuser to wash out the speckle, a more uniform background was obtained (Fig. 5b), with 36±14 counts/100ms or a CV=39%.Focusing on the lower right regions with high signal, the uniformity of background without diffuser was 4408±2279 counts/100ms, CV=52% and the uniformity of background with diffuser was 66±17 counts/100ms, CV=26%.However, in these experiments, diffusing the laser light resulted in 98% loss of signal due to the compromised coupling of the laser light into the fiber and microscope.

Minimizing the dark-field background
Using the diffraction pattern of the graticule, we measured the intensity of the zeroth order (undiffracted light) before and after blocking it with the DMD.The ratio of signal before and after turning the DMD mirrors off was 3200:1.In the imaging plane, the average background intensity was ~934±302 (mean ± standard deviation of all pixels) counts with 2000 ms exposure when blocking the zeroth order with only the DMD in the second conjugate Fourier plane (F" in Fig. 1).To further reduce the dark-field background, we placed a beam stop made of a 0.3mm graphite pencil lead at the center of the first conjugate Fourier plane, F'.When this beam stop was added, the contrast was improved to 4200:1, and the average background intensity was reduced by 30% to ~647±243 counts with 2000 ms exposure (Fig. 6a and 6b).We repeated the initial contrast ratio measurement above (without the graphite beam block) with the DMD rotated by 180°.In this rotated position where the "0" mirrors are off and the "1" mirrors are on, the contrast was 3600:1.Therefore the contrast did not depend significantly on the binary assignment of the on and off mirrors.However, we also found that if light is incident on the entire DMD surface, while only a portion of the mirrors is turned off, stray light generated by the light striking the remaining 'on' mirrors contributes to our measured background at the location corresponding to the 'off' mirrors.This situation is relevant to unfiltered dark-field images where only the zeroth order is blocked while all other orders of diffraction are passed.On the other hand, if we start with all mirrors turned off, and measure contrast at a location corresponding to the portion of the mirrors that are turned on, then the value of the contrast ratio can be as high as 17,000:1.The increase in contrast ratio corresponds to a decrease in background due to the decrease in stray light when all mirrors are initially in the off position.This would be the case for the Gabor filtered images for which the DMD image consists of turning on a portion of the mirrors while all others are turned off.

Sensitivity to object aspect ratio
To evaluate the sensitivity of our DMD-based OSI system to object shape, we implemented a Gabor-like filter bank as described in the Methods section.The filters were centered at 0.805 cycles/µm and spanned orientations 0° ≤ θ < 180°.Optically filtered images of spheres and bacteria were collected and analyzed pixel by pixel for their intensity as a function of filter orientation.Figure 7a-c shows representative dark field images of the objects (E. coli or 0.465µm sphere), and the corresponding polar plots of filter intensity response as a function of filter orientation.The polar plots are shown for a pixel located at the center of the object, although the response plot was similar for all pixels within the object (data not shown).By switching the focal length of lens L4 from 250mm to 50mm, we acquired filtered images at ~0.168µm/pixel ("high mag") and ~0.83µm/pixel ("low mag") respectively, for the E. coli (Fig. 7b and c).The pixel intensity response for the sphere varied little as a function of Gabor filter orientation (Fig. 7d).In contrast, for the E. coli, a maximum response significantly above the average of the responses was obtained at an angle perpendicular to the orientation of the object (Fig. 7e and 6f, filled blue circles).Since the signal was filtered in the Fourier plane, the measurements were not affected by the resolution of the images.Thus, even at low magnification, when the shape of an E. coli could not be discerned in the image, the response plot could still retrieve the same scattering pattern with similar result as for high resolution (Fig. 7e, 7f, compare red squares with blue circles).Also as expected, the orientation, α, of the bacteria in the sample is perpendicular to the Gabor filter orientation, φ, giving maximum response in Fourier space with α=φ+90.Thus, one could in principle retrieve the orientation of the bacteria in the sample by finding the angle at which the Gabor filter response is maximized.We found that for 87% of the bacteria that appeared clearly elongated in the images, the orientation of the bacteria measured from the Gabor filter responses was within 5° of the particle orientation measured directly in the dark field image.
To assess the potential of this method to differentiate a large number of particles, we analyzed the filtered responses of 66 spheres and 60 E. coli.We defined "aspect ratio" as the maximum filtered intensity response over the average of the 18 responses.Figure 8a left panel shows a representative dark field image of a mixture of spheres (D = 0.494µm) and E. coli.In the mixture, we used fluorescent spheres to distinguish them from E.coli.The background was disregarded by setting an intensity threshold based on the dark field image, and aspect ratio was calculated for each remaining pixel.A color-coded image directly encoding aspect ratio is shown in Fig. 8a right panel.The aspect ratio varied on average by 15% for pixels belonging to the same sphere; and on average by 10% for pixels belonging to the same bacterium.In Fig. 8b a pixel histograms based on the "aspect ratio" images is shown for all the spheres and bacteria tested.The plots in Fig. 8b were obtained by manually segmenting the spheres and bacteria in the color-coded "aspect-ratio" images, separately pooling all the sphere segments and bacteria segments, and then plotting a normalized histogram of pixel values for each of the two groups of segments.For each group of segments, pixel numbers were normalized to the total number of pixels in that group.The histogram of spheres has a sharp peak at aspect ratio ~1.5 and the histogram of E. coli has aspect ratio between 2 to 10 due to their varied length and rotation with respect to the optical axis.A student t-test yielded a p value <<0.001 indicating that the histograms are significantly different.

Feasibility of collecting Gabor filtered data within living cells
To evaluate the feasibility of using the DMD-based setup to measure subcellular morphology, we applied the same orientation dependent Gabor filter bank on living iBMK cells.Figure 9ac show differential interference contrast (DIC), dark-field, and Gabor filtered images of two cells.At each pixel, we collected 18 intensity responses for each filter orientation as for the sphere and bacteria data set discussed earlier.Object aspect ratio was again measured by taking the ratio of maximum to average filter response.A threshold was used to remove background pixels for which the average filter response was less than 4000 counts.A color image encoding the value of the measured aspect ratio parameter is shown in Fig. 10a.These data suggest that sufficient signal may be collected from living cells to perform the Gabor based optical filtering.One of the advantages of the optical scatter imaging method in contrast with non-imaging spectroscopy is that the scattering signal can be localized to specific regions within the cells.Thus for example, one can quantify subcellular morphology in situ and correlate the morphological information with biochemical data obtained by fluorescence.To demonstrate this possibility, the cells were labeled with mitotracker green, and we segmented two areas, one in which mitochondria are mostly round and punctate in appearance (Area 1), and the other containing mostly filamentous looking mitochondria (Area 2) (Fig. 10b).Note that the broadband fluorescent emission was collected on a different microscope port and camera to avoid reflection and chromatic aberration at the DMD.Pixel histograms based on the measurement of the "aspect ratio" parameter are shown in Fig. 10c for the two areas.The histograms were normalized to the total number of pixels.Area 1, which has mostly round punctate mitochondria, has more pixels with aspect ratio less than 2; and area 2, which has mostly filamentous mitochondria, has more pixels with aspect ratio higher than 3. Using the student t-test, we found the two areas to be significantly different with p-value << 0.001 indicating the potential for distinguishing different subcellular morphologies.

Discussion
We extended our size-sensitive optical scatter imaging (OSI) method to analyze the shape of the scattering objects.As is the initial OSI system [1], the system relies on analyzing the transform of the sample object.The transform is formed in a Fourier conjugate plane of our imaging system and contains the scatter intensity at every scatter angle collected by the microscope's numerical aperture.However, the previous Fourier filter consisted of a circular iris with variable diameter and only permitted the collection of scatter intensity integrals between a center stop and the outer edge of the iris.In contrast, the DMD Fourier filter used here consists of a 1024x768 array of micro-mirrors 13.7x13.7µm 2 each.When activated by a programmable actuator, the mirrors can be titled in tens of microseconds to deflect the incoming light towards or away from the collection optics.The micro-mirror array therefore acts like an array of shutters, which can be used to pass or block the light scattered at any desired combination of scattering angles within the numerical aperture of the microscope system.This can in turn be used to characterize particle shape by analyzing the scattering pattern in two dimensions.
In this study, we chose a digital micro-mirror device (DMD) for light modulation.Compared with other spatial light modulators, such as liquid crystal devices, the DMD has several advantages, including high efficiency, high contrast ratio, and high mirror actuation speed.However these advantages were offset by specific issues pertaining to the use of the DMD in a conjugate Fourier plane of a microscopic imaging system.In particular, the array of tilted mirrors acts as a blazed grating, which causes significant chromatic aberrations and precludes imaging samples with a broad band emission.This is particularly significant for combining scattering and fluorescence measurement through the DMD on the same microscopy port.Thus in our study, broadband fluorescent images of spheres or cells were collected on a separate camera and post-registered with the scatter images.This problem would not be present using a different spatial light modulator, such as a liquid crystal device (LCD), that does not involve tilted pixels.Preliminary data (not shown) using a lower-end LCD (LC 2002, Holoeye Corp.) confirmed that there are no chromatic aberrations for the LCD.We also found that this 800x600 pixel LCD device did not exhibit the same edgegenerated geometric aberrations that we saw with the DMD (Fig. 3).Despite the expected high throughput and efficiency of the DMD, signal loss was still a problem due to the use of the spinning diffuser to wash out speckle when imaging with the laser source.It is nevertheless important to note that slightly varying the laser source wavelength or the angle of incidence to better match the blaze angle of the DMD could also improve throughput.A comparison between the throughput of a DMD-based system vs. that of a state-of-the-art LCD-based system remains to be fully assessed to select the optimum spatial light modulator for this optical scatter imaging application.One remaining advantage of the DMD over an LCD is the intensity contrast ratio between off and on pixels.This contrast may be around 1:1000 for a state-of-the-art LCD vs. at least 1:3200 for the DMD.This intensity ratio is important in our application, where inefficient blocking of the light at the chosen spatial frequencies can result in significant background and increased noise in the filtered images.
In this report, we used optical Gabor-like filters with various orientations to look for scatter anisotropies with respect to the azimuthal angle of scatter,φ.Using spheres and E. coli, we were able to obtain two populations of particles with distinct aspect ratio values showing the feasibility of applying the Gabor based technique for discrimination of particles based on their roundness.The aspect ratio values were obtained by measuring the aspect ratio of the scattering pattern, which is related to the aspect ratio of the scattering particle.Calibration using particle standard would be needed to establish the relationship between our measured aspect ratio parameter and the actual aspect ratio of the scattering source.Since our method manipulates the scattering signal directly in a conjugate Fourier plane, our measurement is not affected by image resolution.In particular, using the E. coli as a model sample, we also showed that our method could retrieve the pattern of filtered responses in both high and low resolution condition even in highly blurred images (Fig. 7).This is an advantage over digital image analysis, which relies greatly on image resolution.The ability to perform our measurement at low magnification ultimately results in increasing measurement throughput by speeding up image acquisition and enabling the analysis of larger fields of view.
We also demonstrated feasibility of acquiring the filtered data from two subcellular regions containing punctate or filamentous mitochondria, respectively.Our filtered data could differentiate the two regions based on the aspect ratio parameter measured at each pixel, and resulted in a lower aspect ratio measurement in the region with round mitochondria as expected.This is likely due to the fact that mitochondria are responsible for a large part of the scattering signal in the cytoplasm [18].However in general, morphological measurements

Fig. 1 .
Fig. 1.Digital micromirror device-(DMD-) based optical scattering imaging system.The DMD is placed in conjugate Fourier plane F".Unscattered light is blocked at F' and F" (light blue beam).The magnification of the Fourier plane on the DMD is controlled by lenses L2 and L3, while the magnification of the final image was varied by changing the focal length of L4.The imaging beam (red trace) is collimated on the DMD before final focusing onto the charged coupled device (CCD) camera.

Fig. 2 .
Fig. 2. (a) Spheres (0.465µm) imaged using a filtered halogen lamp at 632.8 ± 0.5nm (1500ms exposure).(b) The same spheres imaged using the He-Ne laser at 633nm (300ms exposure).(c) cross section of the signal in panel (a) at dashed red line, (d) cross section of the signal for the same sphere in panel (b).Each pixel corresponds to 0.27µm.

Fig. 3 .
Fig. 3. Dark field image of 0.465 µm spheres with transform occupying (a) 760 mirrors in diameter centered on the DMD, (b) 300 mirrors in diameter centered on the DMD or (c) 300 mirrors in diameter positioned at the upper right hand corner of the DMD.In (c), the DMD was translated so that the center of the shifted active aperture was aligned with the incident beam.Thus, the light reflected from the DMD's active aperture in (c) still passed through the center of L4.In each case, insets show the position of the DMD apertures; the white area indicates 'on' mirrors; the black area 'off' mirrors.

Fig. 4 .
Fig. 4. (a) Field of view showing image overlap due to diffraction at the DMD.The green spots are the pixels chosen as point spread function during deconvolution.Note that the spots were enlarged for clarity, only one pixel at the center of each spot was actually used for the point spread function.(b) Same image as in (a) after deconvolution.(c) pixel histograms of the areas within the red and blue squares in panel (a).(d) pixel histograms of the same image areas in panel (b).

Fig. 5 .
Fig. 5. Images of the background using the He-Ne laser as light source (a) without the spinning diffuser (100ms exposure), and (b) with spinning diffuser (2000ms exposure).The background consisted of a water sample sandwiched between a microscope slide and coverslip.Lower panels show the cross section of the signal at the red dashed line in each corresponding image.

Fig. 6 .
Fig. 6.Images of a water sample sandwiched between a microscope slide and cover slip collected without (a) and with (b) the center stop at F'(see Fig. 1) 2000ms exposure.

Fig. 7 .
Fig. 7. Dark field images of (a) 0.465µm sphere, and (b), (c) E. coli and high and low magnification.Corresponding intensity response, ρ, of a pixel located at the center of the object as a function of Gabor filter orientation, φ, for (d) the sphere and (e) & (f) the E. coli (e corresponds to b; f to c).The symbols connected by the solid line represent the measured data points.The dotted line indicates the expected diametrically symmetric responses at the complex conjugate frequency positions of the Gabor-like optical filters.In (e) and (f) the responses were normalized to the maximum intensity.

Fig. 8 .
Fig. 8. (a) Left panel: representative dark-field image showing the location of fluorescent spheres (green) and unstained bacteria (red arrowheads).Right panel: color coded image of the bacteria-sphere mixture.The color scale corresponds to the aspect ratio parameter taken as the ratio of maximum intensity to average intensity response.(b) Aspect ratio distributions for the 66 spheres and 60 E. coli tested.

Fig. 10 .
Fig.10.Images of same iBMK cells as in Fig.9(a) color coded image encoding aspect ratio of scattering response at each pixel.The aspect ratio was measured as maximum/average intensity of filtered responses, (b) Mitotracker Green fluorescence to visualize specifically the mitochondria.The two segmented areas include round and punctate mitochondria (Area 1) or filamentous looking mitochondria (Area 2).(c) Aspect ratio distribution for the pixels in Area 1 and Area 2. Pixel numbers were normalized to the total number of pixels within each area.