Optically Computed Optical Coherence Tomography

Abstract

An optically computed optical coherence tomography (OC-OCT) technology is disclosed. The OC-OCT system performs depth resolved imaging by computing the Fourier transform of the interferometric spectra optically. The OC-OCT system modulates the interferometric spectra with Fourier basis function projected to a spatial light modulator and detects the modulated signal without spectral discrimination. The optical computation strategy enables volumetric OCT imaging without performing mechanical scanning and without the need for Fourier transform in a computer. OC-OCT performs Fourier transform signal processing optically, without the need of mechanical scanning, and before data acquisition unlike traditional OCT methods and systems. The scan-less OCT imaging is achieved through the use of spatial light modulator (SLM) that precisely manipulates light wave to generate output with desired amplitude and phase.

Claims

1. A method for optically computed optical coherence tomography (OC-OCT), comprising: performing a depth resolved image of an object by an optically computed optical coherence tomography (OC-OCT) system; optically computing a Fourier transform of an interferometric spectra and performing signal processing of the image before image data acquisition, unlike conventional OCT wherein image data acquisition is performed before signal processing; and wherein the OC-OCT system eliminates mechanical scanning in tomographic imaging and performs computation optically of the image without requiring transfer of image data into a computer to perform computation tasks for image reconstruction and data analysis.

2. The method claim 1, further includes: using a spatial light modulator (SLM) to manipulate a light wave to generate output with a desired amplitude and phase for computation and to produce a scan-less three dimensional (3D) OCT image.

3. The method of claim 2, wherein the optical computation of the Fourier transform further includes modulating the interferometric spectra with the SLM that is programmable, and then performing spectrally non-discriminative detection of the object.

4. The method of claim 1, further comprising modulating the interferometric spectra with Fourier basis function projected to a spatial light modulator (SLM) and detecting the modulated signal without spectral discrimination.

5. The method of claim 1, wherein the OC-OCT system manipulates optical signals in both spatial and spectral domain for computation.

6. The method of claim 1, further includes observing transient phenomena in the object selected from a group consisting of neural activity, blood flow dynamics, and any combination thereof.

7. The method of claim 1, wherein the imaging is done on a biological tissue.

8. The method of claim 7, wherein the biological tissue is soft tissue, and wherein the soft tissue is deep tissue selected from the group consisting of breast tissue, skin, brain tissue, muscles, tendons, ligaments, connective tissue, lung tissue, liver tissue, kidney tissue, intestinal tissue, stomach tissue, heart tissue, bladder tissue, pancreatic tissue, spleen tissue, and any combination thereof.

9. The method of claim 1 further includes obtaining in situ 3D imaging of the biological tissue.

10. The method of claim 1 further includes extracting a signal from a specific depth in the object directly without signal processing in a computer; and wherein depth resolution is by optically Fourier transforming a spectral interferogram.

11. The method of claim 1 further includes phase resolved volumetric OCT imaging without mechanical scanning, and imaging an arbitrary 2D plane in a snapshot manner.

12. A method for optically computed optical coherence tomography (OC-OCT), comprising performing depth resolved imaging by computing a Fourier transform of an interferometric spectra optically; modulating the interferometric spectra with Fourier basis function projected to a spatial light modulator (SLM) and detecting the modulated signal without spectral discrimination.

13. An optically computed optical coherence tomography (OC-OCT) system, comprising an optical computation module for directly outputting a depth resolved OCT signal of an object, a low coherence interferometer in communication with the optical computation module for imaging the object; wherein, the optical computation module including a spatial light modulator (SLM) sized to manipulate a light wave to generate output with a predetermined amplitude and phase; and wherein the optical computation module in OC-OCT performs Fourier transform optically before data acquisition by calculating an inner product between a Fourier basis function projected by the spatial light modulator (SLM) and a Fourier domain interferometric signal.

14. The optically computed optical coherence tomography (OC-OCT) system of claim 13, wherein the spatial light modulator (SLM) enables volumetric three dimensional (3D) OCT imaging without performing mechanical scanning and without the need for Fourier transform in a computer.

15. The optically computed optical coherence tomography (OC-OCT) system of claim 13, wherein the optical computation module further includes a polarization beam splitter (PBS) in communication with a beam splitter (BS) in the low coherence interferometer.

16. The optically computed optical coherence tomography (OC-OCT) system of claim 13, wherein the low coherence interferometer further includes a broadband source to illuminate the interferometer.

17. The optically computed optical coherence tomography (OC-OCT) system of claim 13, wherein the low coherence interferometer further includes a reference mirror and a sample arm for the object being scanned.

18. The optically computed optical coherence tomography (OC-OCT) system of claim 13, wherein the SLM is a programmable SLM; and the optical computation of Fourier transform is achieved by modulating the interferometric spectra with the programmable SLM and then performing spectrally non-discriminative detection.

19. The optically computed optical coherence tomography (OC-OCT) system of claim 13, wherein the optically computed optical coherence tomography (OC-OCT) system is used for a clinical diagnosis.

20. The optically computed optical coherence tomography (OC-OCT) system of claim 13, wherein the optically computed optical coherence tomography (OC-OCT) system images an arbitrary 2D plane in a snapshot manner.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawings(s) will be provided by the Office upon request and payment of the necessary fee.

[0019] To assist those of skill in the art in making and using the disclosed optically computed optical coherence tomography and associated systems and methods, reference is made to the accompanying figures, wherein:

[0020] FIGS. 1A-1B show (a) a schematic of a conventional OCT system generating a Bscan using multiple Ascans; (b) is a schematic of a conventional OCT system generating a Cscan using multiple B scans;

[0021] FIGS. 2A-2C show (a) data flow in a conventional FD OCT system; (b) shows data flow in an OCT system, in accordance with one embodiment of the present disclosure; (c) shows data flow in Fourier transform of spectral interferogram;

[0022] FIG. 3 shows one embodiment of an OC-OCT system;

[0023] FIGS. 4A-4B show (a) is a graphical depiction of an Ascan obtained from a mirror at different depths; (b) is a graphical depiction of a linear relationship between the n.sub.R and the actual depths;

[0024] FIGS. 5A-5F show (a) “en face image” of USAF 1951 resolution target; (b) the 6.sup.th element of the 8.sup.th group in the resolution target can be resolved; (c) the top part of SLM was programed to obtain OCT signal from the resolution target; (d)-(f) en face images of the resolution target when the plane chosen by the SLM moved away from the sample surface;

[0025] FIGS. 6A-6D show an OC-OCT image of onion skin cells at different depths (a), (b), and (c); (d) image generated by averaging signal at different depths, wherein the scale bars represent 50 μm;

[0026] FIGS. 7A-7G show (a) 3D rendering image of 3D phantom; en face image from the substrate (b) and the top of photoresist layer (c); (d) en face image generated by averaging OC-OCT signal within a depth range of 36 μm; (e)-(g) cross sectional images of three positions indicated by red lines in FIG. 7 (d), wherein the scale bars represent 300 μm; and

[0027] FIGS. 8A-8B show (a) optical computation of Fourier transform by modulating M with ƒ.sub.n projected by the SLM and performing spectrally integration; (b) snap-shot phase imaging by projecting cosine and sin patterns to the SLM.

DETAILED DESCRIPTION

[0028] Exemplary embodiments are directed to an Optically Computed-Optical Coherence Tomography (OC-OCT) system and process of using same. It should be understood that different embodiments could generally be applied. Optically computed OCT (OC-OCT) technology disclosed herein eliminates the need for mechanical scanning in 3D OCT imaging by employing a highly novel optical computation system to perform Fourier transform. For conventional Fourier domain OCT, data is acquired and transferred to PC where Fourier transform is performed to reconstruct depth profiles of the sample. OC-OCT performs signal processing optically before the signal is detected by the camera.

[0029] The optical computation procedure is achieved by using a spatial light modulator (SLM). SLM is known as being used in other applications such as optical pulse shaping, structured illumination, and optical computation. However, SLM has not been used in OCT imaging until now. Using SLM, light wave can be precisely modulated to have the anticipated amplitude and phase. The spectral interferogram output from a spectral domain OCT system is modulated by a programmable SLM to achieve Fourier transform optically. The signal is later detected without spectral discrimination. An optically computed two-dimensional image at a specific depth determined by the SLM pattern is thus produced. The optical computation strategy allows volumetric OCT imaging without axial or lateral mechanical scanning that is novel and has not been demonstrated before in this field.

[0030] Adverting to the figures, FIG. 3 shows one embodiment of an OC-OCT system that could include an optical computation module 301 having a spatial light modulator (SLM) 302, a polarization beam splitter (PBS). The OC-OCT system may also include a low coherence interferometer 303 having a beam splitter (BS), and a broadband source to illuminate the interferometer. The low coherence interferometer may also further include a reference mirror 304 and a sample arm 305 for the object (OBJ) being scanned. In the present embodiment, the SLM is sized to precisely manipulate a light wave to generate output with a desired amplitude and phase. In one embodiment, optical computation of Fourier transform is achieved by modulating the interferometric spectra with a programmable SLM and then performing spectrally non-discriminative detection.

[0031] OC-OCT is a Fourier domain technique that achieves depth resolution by optically Fourier transforming spectral interferogram. Consider an Ascan S (S∈.sup.N and S=[s.sub.1, s.sub.2, s.sub.3, . . . , s.sub.N].sup.T). With sample light originating from a specific transverse coordinate, the interferometer generates a spectral interferogram M after a disperser. M is a 1D vector (M∈.sup.N and M=[m.sub.1, m.sub.2, m.sub.3, . . . , m.sub.N].sup.T) and is mathematically related to the spatial domain Ascan through Fourier transform: S=FM which is more explicitly shown in Eq (1) (s.sub.n represents spatial domain OCT signal at the n.sup.th discrete depth in an Ascan; m.sub.k represents spectral signal at the k.sup.th wavenumber; F∈.sup.N×N is the Fourier transform matrix and Fnk=e.sup.j2πnk/N).

[00001]$\begin{array}{cc}\left[\begin{array}{c}{s}_1\\ s_2\\ \mathrm{.Math.}\\ s_N\end{array}\right]=\left[\begin{array}{cccc}{F}_{11}& F_{12}& \mathrm{.Math.}& F_{1N}\\ F_{21}& F_{22}& \mathrm{.Math.}& F_{2N}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ F_{N1}& F_{N2}& \mathrm{.Math.}& F_{\mathrm{NN}}\end{array}\right]\left[\begin{array}{c}{m}_1\\ m_2\\ \mathrm{.Math.}\\ m_N\end{array}\right]& \left(1\right)\end{array}$

[0032] As illustrated in FIG. 2A, a conventional FD OCT system measures the entire interferometric spectrum M that has N discrete Fourier bins, streams the data into a computer, performs Fourier transform in the computer and reconstructs the entire Ascan. FIG. 2A also implies N Fourier bins have to be acquired to fully reconstruct the Ascan S, even if a small subset of pixels are of interest in the Ascan. OC-OCT takes a completely different approach to resolve a pixel in 3D space. One embodiment of the method performed by the OC-OCT system is shown in FIG. 2B.

[0033] According to the above Equation (1), s.sub.n, the OCT signal at the n.sup.th discrete depth in an Ascan, can be expressed in Eq (2) that shows s.sub.n is the inner product between vector ƒ.sub.n (the transpose of n.sup.th row of the Fourier matrix F) and vector M. In Eq (2), .Math. indicates vector inner product.

[00002]$\begin{array}{cc}{s}_n=F_{n1}{m}_1+F_{n2}{m}_2+\mathrm{.Math.}+F_{\mathrm{nN}}{m}_N=\left[\begin{array}{cccc}{F}_{n1}& F_{n2}& \mathrm{.Math.}& F_{\mathrm{nN}}\end{array}\right]\left[\begin{array}{c}{m}_1\\ m_2\\ \mathrm{.Math.}\\ m_N\end{array}\right]=f_n.Math.M& \left(2\right)\end{array}$

[0034] Equation (2) provides an alternative approach to address a spatial location in OCT imaging. As illustrated in FIG. 2 (b), the OC-OCT system in this embodiment calculates ƒ.sub.n.Math.M optically and directly obtains s.sub.n at the point of data acquisition. Optical computation of Eq (2) is further illustrated in FIG. 2 (c). The chosen Fourier basis function (ƒ.sub.n) is projected to the SLM along the dimension of spectral dispersion. The spectrum modulated by the SLM is essentially the element-wise product of ƒ.sub.n and M (ƒ.sub.n∘M). The detector then performs spectrally non-discriminative detection, generating s.sub.n, the inner product between vector ƒ.sub.n and vector M.

[0035] The configuration of one embodiment of an OC-OCT system that allows depth resolved imaging with an extended field of view is illustrated in FIG. 3. The OC-OCT system could include a broadband source to illuminate the Michaelson interferometer with an extended field of view. A 2D reflective SLM is used for light modulation and a 2D camera is used for signal detection in this embodiment.

[0036] The imaging principle of the OC-OCT system is explained as follows. First, the OC-OCT configuration in FIG. 3 establishes a one-to-one mapping between the transverse spatial coordinate at the sample plane and at the detector plane, illustrated as solid and dashed light beam profiles in FIG. 3. This is similar to conventional light microscopy. Optical signal originating from transverse coordinate (x.sub.0,y.sub.0) at the sample is mapped to the same y coordinate (y=y.sub.0) at the detector, because the light beam is not altered along y dimension by the grating or the SLM. On the other hand, the spectrum originating from different x coordinate arrives at the SLM plane with a global shift proportional to the x coordinate after the diffraction grating.

[0037] Reflected by the SLM and diffracted again by the grating, the light rays originating from (x.sub.0,y.sub.0) at the sample are collimated and eventually focused to (x.sub.0,y.sub.0) at the detector plane for spectrally non-discriminative detection, for a magnification of 1 from the sample plane to detector plane without loss of generality. On the other hand, depth resolution is achieved through optical computation. The diffraction grating disperses the output of the interferometer along x direction and the SLM projects a Fourier basis function (ƒ.sub.n) to its row at a specific y coordinate (y=y.sub.0), as illustrated in the upper right inset of FIG. 3. Spectral interferogram originating from different x coordinate at the sample is modulated by a laterally (in x dimension) shifted version of ƒ.sub.n, which does not affect the results of optical computation of OCT signal magnitude. Spectrally non-discriminative detection of the modulated interferometric spectrum generates depth resolved OCT signal from the n.sup.th discrete depth, for pixels corresponding to different x coordinates. Notability, when all the rows of the SLM projects the same pattern for spectral modulation, the OC-OCT system generates an en face imaging from a specific depth. If different rows of the SLM project different Fourier basis functions, signals can be simultaneously obtained from different depths. Therefore, OC-OCT allows snap-shot imaging from an oblique plane (the green plane in FIG. 1B).

[0038] In one embodiment, the OC-OCT system shown in FIG. 3 could include a mounted LED (Thorlabs) at 470 nm with 25 nm bandwidth as the broadband source. The interferometric spectrum was dispersed by a 600/mm grating, modulated by a 2D SLM (Holoeye LC-R 720), and detected by a CMOS camera (Basler acA2000). The achromatic doublet lens in front of the SLM had a focal length of 250 mm and the achromatic doublet lens in front of the CMOS camera had a focal length of 100 mm. Identical objectives (20× Olympus, dry) were used in reference and sample arms of the interferometer.

[0039] To demonstrate 3D OC-OCT imaging within a large depth range, achromatic doublet was used as imaging objectives to obtain results shown in FIG. 7. Notably, a polarized beam splitter (PBS) was inserted between the Michaelson interferometer and the optical computation module to ensure unambiguous amplitude modulation by the SLM and direct optical signal for detection. In FIGS. 6A-6D demonstrated is OC-OCT images of onion skin cells at different depths (a), (b), and (c); (d) image generated by averaging signal at different depths, wherein the scale bars represent 50 μm.

[0040] Prior to imaging experiments, the present inventors calibrated K(k) the mapping between the pixel index (k) in a row of SLM and the corresponding wavenumber K, because the pixels in a row of the SLM generally do not sample wavenumber domain spectral data uniformly. The calibration was achieved by measuring the interferometric spectrum obtained from a specular sample and enforcing linear phase [12]. The present inventors also calibrated R(v), the mapping between the value v projected to SLM pixels and the actual light reflectivity (R) of the SLM, because R(v) depends on the wavelength and polarization of the incident light, and is generally nonlinear. When v takes value of Fourier basis function (F.sub.nk in Eq (1)) and is directly projected to the k.sup.th pixel in a row of SLM pixels, the spectral modulation is non-sinusoidal, leading to diminished signal amplitude and ghost high harmonic peaks after optical Fourier transformation. To ensure that precise sinusoidal modulation was imposed to the interferometric spectrum, the present inventors projected the value of R.sup.−1(F.sub.nK(k)) to the k.sup.th pixel in a row of SLM pixels. Moreover, the SLM cannot directly generate complex exponential function needed in Fourier transform (Eqs (1) and (2)). Therefore, the present inventors projected cosine and sine patterns (F.sub.cos(cos(2πnK(k)/N)+1)/2 and F.sub.sin=(sin(2πnK(k)/N)+1)/2) to the SLM. The present inventors temporally interlace ƒ.sub.cos (F.sub.cos with k=1, 2, 3, . . . ) and ƒ.sub.sin (F.sub.sin with k=1, 2, 3, . . . ) for spectral modulation, synchronized the data acquisition with the alternation of cos and sin patterns, acquired signals from cosine and sine channels (s.sub.cos=ƒ.sub.cos.sup.TM−s.sub.DC and s.sub.sin=ƒ.sub.sin.sup.TM−s.sub.DC) and extracted the magnitude of the OC-OCT signal: I=(s.sub.cos.sup.2+s.sub.sin.sup.2).sup.1/2. With reference light much stronger than sample light, s.sub.DC could be estimated by Σm.sub.k obtained with sample arm blocked. To simplify subsequent description, the present inventors refer the function projected to the SLM as ƒ.sub.n that was generated after wavenumber calibration, reflectivity calibration, and temporal interlacing.

[0041] The present inventors first experimentally validated the z sectioning capability of the OC-OCT system. The present inventors assessed the axial point spread function (PSF) of the OC-OCT imaging system, using Ascans obtained from a mirror with an impulse reflectivity profile. The present inventors projected a series of complex exponential functions (ƒ.sub.n, n=1, 2, 3, . . . ) to different rows (different y coordinate) of SLM pixels. As a result, different rows of the detector received signals modulated by different complex exponential functions and came from different depths of the sample. The axial PSF (a 1D vector) was then obtained by averaging the image directly obtained from the camera along x direction. The present inventors varied the axial position of the mirror using a translation stage, and obtained axial PSFs as shown in FIG. 4A. The horizontal axis at the bottom of FIG. 4A is the row index (n.sub.R) of the sensor array and is linearly related to the depth z: z=an.sub.R+b. The present inventors correlated the peak pixel index with the actual axial position of the sample (FIG. 4B) and extracted the values for a and b through linear fitting (a≈0.17 μm and b≈36.91 μm) that allowed the present inventors to convert n.sub.R to actual depth shown as the horizontal axis at the top of FIG. 4A. To evaluate the axial resolution, the present inventors used a Gaussian envelop to fit the PSFs obtained at different depths and the axial resolution of the OC-OCT system was estimated to be 5 μm according to the full width half maximum (FWHM) of the Gaussian function. The experimental axial resolution was slightly inferior to the theoretical axial resolution (δz=0.44λ.sub.0.sup.2/Δλ=3.9 μm given λ.sub.0=470 nm and Δλ=25 nm), probably because various optical components resulted in a smaller effective spectral bandwidth.

[0042] The present inventors demonstrated the capability of the OC-OCT system for depth resolved en face imaging. To achieve en face slicing of the sample at depth z.sub.0, the present inventors projected the same modulation pattern (ƒ.sub.n0) to different rows of the SLM. The present inventors brought the sample, a USAF1951 resolution target, to depth z.sub.0 (z.sub.0=32.30 μm) and obtained the image shown in FIG. 5A. The area within the red square is enlarged in FIG. 5 (b), in which the smallest discernable structure is the 6.sup.th element of the 8.sup.th group, suggesting a lateral resolution of 2.2 μm. To validate the image in FIG. 5A was indeed sectioned through optical computation, the present inventors projected ƒ.sub.n0 to the top rows of the SLM and projected a constant value to pixels at the bottom rows of the SLM. The sample remained at depth z.sub.0 and other settings remained unchanged. The resultant OC-OCT image (FIG. 5C) shows large brightness at the top and appears to be completely dark at the bottom. In FIGS. 5D, 5E, and 5F, the present inventors further compared en face images obtained from the resolution target when the SLM modulation pattern selected different imaging depths (z.sub.0=32.30 μm, z.sub.0+1.25 μm, z.sub.0+2.5 μm). When the virtual plane determined by the SLM moved away from sample surface, the brightness of OC-OCT image decreases.

[0043] The present inventors also demonstrated OC-OCT for 3D imaging using onion skin cells. The present inventors projected the same Fourier basis function to different rows of the SLM to obtain en face OCT image at a specific depth. By varying the Fourier basis function, the present inventors obtained en face images at different depths in FIGS. 6A, 6B, and 6C with 5 μm axial displacement in between. FIG. 6D is the image obtained by averaging OC-OCT signals within a depth range of 15 μm.

[0044] The present inventors also obtained 3D rendered volume through OC-OCT imaging. The present inventors designed lateral patterns on a laser-plotted polyester-based photomask, and fabricated a 3D phantom by depositing photoresist layer (SU-8 2035) with 37 μm elevation on silicon substrate using the photolithography facility at Brookhaven National Laboratory. The present inventors changed the modulation function projected to the SLM to acquire en face OC-OCT data from different depths for volumetric imaging. With 2D images obtained from different depth (29 en face images obtained with a 1.25 μm axial interval), a 3D rendered volume is obtained. FIGS. 7A, 7B and 7C show images corresponding to the surface of silicon substrate and the top of the deposited pattern. FIG. 7D is the image generated by averaging OC-OCT signal at different depths. Along the red lines in FIG. 7D, the present inventors generated cross sectional images (FIGS. 7E, 7F and 7G) using the volumetric data. The rectangles in FIGS. 7E, 7F and 7G correspond to depth profiles for the areas within rectangles of FIG. 7D, from which the top of the letters “I” and “T”, middle of the letter “N” and bottom of the letter “J” are discernable.

[0045] The OC-OCT system described in the present disclosure enabled optically computed 3D OCT imaging for the first time to the best of the present inventors' knowledge. OC-OCT is fundamentally different from existing technologies that take transverse plane as the preferential scanning dimension. For optical coherence microscopy (OCM) and full field OCT, mechanical scanning cannot be eliminated. One significant advantage of OC-OCT is its flexibility in data acquisition.

[0046] In one embodiment of the present disclosure, the present inventors performed 3D imaging by projecting the same Fourier basis function to different rows of the SLM and sequentially acquiring en face images at different depths. If fast imaging is needed in an oblique plane, the OC-OCT system can project different Fourier basis to different rows of the SLM and make the oblique plane the dimension for preferential data acquisition. For structural OCT imaging, the present inventors measured the real and imaginary parts of complex OCT signal with the SLM generating cosine and sine modulations and calculated the amplitude of OCT signal. The real and imaginary parts of complex OCT signal can also be used for phase resolved imaging that is sensitive to nanometer scale displacement, in applications such as optical coherence elastography and imaging cell dynamics. The current OC-OCT system generated temporally interlace cosine and sine patterns for spectral modulation. Hence, its imaging speed was limited by the speed of the SLM (60 Hz refreshing rate). To fully utilize the speed of the camera, complex modulation of interferometric spectrum can also be achieved by projecting spatially interlaced cosine and sine patterns to the SLM.

[0047] Optical Computation (OC) for Snap-Shot Phase Resolved OCT Imaging.

[0048] The inventive OC-OCT allows snap-shot imaging from an oblique plane. In the OCC-OCT system, the reference light and sample light superimpose and go through an optical computation module that directly outputs depth resolved OCT signal. Within the optical computation module, interferometric light is first diffracted by a grating. The spectral interferogram M (M∈.sup.N and M=[m.sub.1, m.sub.2, m.sub.3, . . . , m.sub.N].sup.T) is then modulated by the spatial light modulator (SLM) (FIG. 8A)). The SLM generates a temporally static modulation pattern, with different transmittance at different pixels. The transmittance is precisely controlled by the value projected to SLM pixels. M is mathematically related to Ascan (complex vector S∈.sup.N and S=[s.sub.1, s.sub.2, s.sub.3, . . . , s.sub.N].sup.T) at a specific transverse coordinate through Fourier transform: S=FM, where F∈.sup.N×N is the Fourier transform matrix and F.sub.nk=e.sup.j2πnk/N. Conventional Fourier domain OCT imaging obtains an Ascan by acquiring the entire spectral interferogram and performing Fourier transform in a computer. For optical computation, we consider the signal at the n.sup.th discrete depth in an Ascan (s.sub.n) that can be expressed as s.sub.n=ƒ.sub.n.Math.M where .Math. indicates vector inner product and ƒ.sub.n=[F.sub.n1,F.sub.n2,F.sub.n3, . . . , F.sub.nN]′. As illustrated in FIG. 8A, the SLM modulates the interferometric spectrum (M) with ƒ.sub.n, resulting in elementwise product between these two vectors (M⊙ƒ.sub.n).

[0049] Modulated by the SLM and diffracted again by a second grating, the light rays originating from the same transverse coordinate at the sample are collimated and detected without spectral discrimination to generate s.sub.n (FIG. 8A). Furthermore, to extract the phase of the complex signal s.sub.n through snap-shot measurement, it is essential to perform Fourier transform using ƒ.sub.n with complex elements. However, the SLM imposes real modulation of light intensity. To address this issue, the SLM generates interlaced cosine (ƒ.sub.cos,n) and sine (ƒ.sub.sin,n) functions in its rows along y direction (FIG. 8B), and optically computes the real and imaginary parts of the complex OCT signal.

[0050] For structural OCT imaging, the real and imaginary parts of complex OCT signal are measured with the SLM generating cosine and sine modulations and calculated the amplitude of OCT signal. To demonstrate complex OCT imaging, used was the cosine and sine channels output from the OC-OCT system to generate the amplitude and phase of complex signal. The same modulation pattern (f.sub.n0) was projected to all the rows of the SLM to generate OC-OCT signal from depth z.sub.0. Used then was the OC-OCT system to image the substrate and the top of the 3D phantom fabricated by photolithography. In summary, the OC-OCT system described enabled optically computed complex OCT imaging for the first time to the best of the inventor's knowledge.

[0051] The present inventors designed the magnification from the sample plane to the SLM plane, such that the diffraction limited spot size at the sample is mapped to more than two SLM pixels. As a result, the binning of SLM pixels in y dimension to extract complex OCT signal will not lead to reduced axial resolution.

[0052] By taking snapshot measurement of g∈.sup.Nx×Ny, the magnitude (Eq (3))

I.sub.i,j=√{square root over (g.sub.i,2j.sup.2+g.sub.i,2j-1.sup.2)}  (3)

[0053] wherein I.sub.i,j is the magnitude of complex OCT signal and is proportional to the optical field reflected or scattered from the sample, and g.sub.i,2j and g.sub.i,2j-1 are snapshot measurements taken at different rows of the camera, modulated by the SLM with sinusoidal signals with a 90 degree phase difference;

[0054] and phase (Eq (4)) of the complex OCT signal,

[00003]$\begin{array}{cc}{\varphi }_{i,j}=\mathrm{atan}\left(\frac{g_{i,2j}}{g_{i,2j-1}}\right)& \left(4\right)\end{array}$

[0055] wherein ϕ.sub.i,j is the phase of the complex OCT signal and g.sub.i,2j and g.sub.i,2j-1 are snapshot measurements taken at different rows of the camera, modulated by the SLM with sinusoidal signals with a 90 degree phase difference;

[0056] as well as the sub-nanometer displacement used for dynamic imaging (Eq (5)), can be extracted,

[00004]$\begin{array}{cc}{d}_{i,j}=\frac{{\lambda }_0}{4n\pi }\mathrm{atan}\left(\frac{g_{i,2j}}{g_{i,2j-1}}\right)& \left(5\right)\end{array}$

[0057] wherein d.sub.i,j is the subnanometer displacement, λ.sub.0 is an initial signal, n is the refractive index, and g.sub.i,2j and g.sub.i,2j-1 are snapshot measurements taken at different rows of the camera, modulated by the SLM with sinusoidal signals with a 90 degree phase difference.

[0058] Notably, for pixels at different transverse coordinates, the signal formation mechanism remains the same as described above, because the optical computation module establishes a one-to-one mapping between transverse coordinates (x and y) at the sample plane and those at the detector plane (illustrated as solid and dashed light beam profiles in FIG. 8A). Hence the 2D output of the optical computation module is OCT signal from an en face plane at the n.sup.th descrite depth of ƒ.sub.n is projected by the SLM. A different axial position can be selected by projecting a different Fourier basis function.

[0059] While exemplary embodiments have been described herein, it is expressly noted that these embodiments should not be construed as limiting, but rather that additions and modifications to what is expressly described herein also are included within the scope of the invention. Moreover, it is to be understood that the features of the various embodiments described herein are not mutually exclusive and can exist in various combinations and permutations, even if such combinations or permutations are not made express herein, without departing from the spirit and scope of the invention.

REFERENCES

[0060] 1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, “Optical coherence tomography,” science 254, 1178-1181 (1991). [0061] 2. Y. Jia, S. T. Bailey, D. J. Wilson, O. Tan, M. L. Klein, C. J. Flaxel, B. Potsaid, J. J. Liu, C. D. Lu, and M. F. Kraus, “Quantitative optical coherence tomography angiography of choroidal neovascularization in age-related macular degeneration,” Ophthalmology 121, 1435-1444 (2014). [0062] 3. Y. Qiu, Y. Wang, Y. Xu, N. Chandra, J. Haorah, B. Hubbi, B. J. Pfister, and X. Liu, “Quantitative optical coherence elastography based on fiber-optic probe for in situ measurement of tissue mechanical properties,” Biomedical Optics Express 7, 688-700 (2016). [0063] 4. T. Akkin, D. Landowne, and A. Sivaprakasam, “Detection of neural action potentials using optical coherence tomography: intensity and phase measurements with and without dyes,” Frontiers in neuroenergetics 2, 22 (2010). [0064] 5. M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734-1746 (2005). [0065] 6. R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11, 889-894 (2003). [0066] 7. M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11, 2183-2189 (2003). [0067] 8. D. R. Solli and B. Jalali, “Analog optical computing,” Nature Photonics 9, 704 (2015). [0068] 9. W. Zhang, X. Zhang, C. Wang, W. Liao, S. Ai, J. Hsieh, N. Zhang, and P. Xue, “Optical computing optical coherence tomography with conjugate suppression by dispersion,” Opt. Lett. 44, 2077-2080 (2019). [0069] 10. C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, Laser & Photonics Reviews. 5(1):81-101 (2011). [0070] 11. Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nature Communications 6, 6225 (2015). [0071] 12. X. Liu, M. Balicki, R. H. Taylor, and J. U. Kang, “Towards automatic calibration of Fourier-Domain OCT for robot-assisted vitreoretinal surgery,” Opt. Express 18, 24331-24343 (2010).