System, apparatus, and method for improved imaging and holography

Abstract

Incoherent FINCH holography is a simple single shot 3D super resolution imaging method based upon interference of two beams of unfocused light from a subject in focus. The inventors have discovered that in practice, high uniformity (symmetry) between the above and below focus interfering individual beams is important to produce the highest resolution distortion free FINCH holographic based microscopic images. In the case of holographic microscopy, many microscope objectives do not provide the aberration free and unstructured featureless defocused beam, that is identical and symmetrical both above and below the plane of focus, which is optimal for incoherent holography. Microscope objectives have been generally designed to give optimal resolution and results at the plane of focus without primary design concern for aberrations in the defocused beams above and below the plane of focus. Apparatuses and techniques to achieve the appropriate characteristic of symmetrical defocused beams above and below the focal plane for incoherent holography are introduced.

Description

[0001] System, Apparatus, and Method for Improved Imaging and Holography

[0002] Cross-Reference to Related Applications

[0003] This application claims the benefit of priority from U.S. Provisional Application No. 63 / 435,247 filed on December 24, 2022, the entire content of which is hereby incorporated by reference.

[0004] Technical Field

[0005] This disclosure relates generally to optical equipment, and more particularly to optical arrangements that generate holograms.

[0006] Background

[0007] The inventors of the subject matter in this disclosure include an inventor of the Fresnel Incoherent Correlation Holography (FINCH) techniques and systems that are described in, for example, US Patent No. 8,179,578 Filed July 18, 2006. The inventors of FINCH also published several papers describing the FINCH system and technique. See, for example, Joseph Rosen and Gary Brooker, "Digital spatially incoherent Fresnel holography", Optics Letters, Vol. 32, No. 8, April 15, 2007. The contents of US Patent No. 8,179,578 and the publication "Digital spatially incoherent Fresnel holography" are each incorporated by reference in their respective entireties.

[0008] The inventors of the subject matter described in this application subsequently improved upon the original FINCH technique described in US Patent No. 8,179,578, leading to, in one particularly improved implementation, using one or more birefringent lenses as part of FINCH to achieve super resolution in the obtained holographic images. US patent No. 10,228,655 (which claims priority to US Provisional Application No. 61 / 886,064 filed on Oct 3, 2013) describes FINCH using a liquid crystal lens (which is also birefringent). The use of a birefringent crystal lens in FINCH was described in a provisional application that was filed May 1, 2014, which subsequently claimed priority to US Patent Nos. 10,591,870, 10,423,123, and 10,289,070. This novel use of a birefringent lens in FINCH was also described in Nisan Siegel, Vladimir Lupashin, Brian Storrie and Gary Brooker, "High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers", Nature Photonics, 14, 802-808 November 2016. Further developments in the phase shifting procedure used in the recording of FINCH holograms is described in PCT patent application No. PCT / US20201040683 as well as in Nisan Siegel and Gary Brooker, "Single shot holographic super-resolution microscopy," Optics Express 29, 15953-15968 (2021). The contents of US Patent No. 10228655, US. Patent No. 10289070, US Patent Nos. 10 / 591870, 10 / 423123, "High- magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers / ' PCT / US20201040683, and "Single shot holographic super-resolution microscopy" are each incorporated by reference in their respective entireties. While the incorporated documents provide a thorough explanation of FINCH, a brief description of FINCH is provided below for convenience. One skilled in the art will realize that while the following discussion is recited in the context of visible light, any other wavelengths of electromagnetic radiation can be used similarly with imaging components optimized for the other wavelengths.

[0009] FINCH is a single beam interferometric method that can create an interference pattern (also referred to as a hologram or a recorded hologram or a raw hologram) from visible light or any kind of electromagnetic radiation, either incoherent or coherent. In order to obtain a complex-valued 3D image representation of a scene captured by the FINCH technique (also referred to as a complex hologram), a plurality of holograms must be recorded. This plurality of recorded holograms or interference patterns must include at least two "phase shifted" holograms, each with a unique phase factor. The plurality of holograms is typically obtained in a serial manner or simultaneously in a parallel manner by a variety of beam-splitting techniques.

[0010] Figure 1 illustrates a generalized FINCH imaging system. An object (also referred to as sample) 101 emits or reflects light toward the FINCH optical system 102, which receives the light through a lens or other aperture and produces (from any single received beam of light) two co-propagating beams denoted Beam 1 and Beam 2, or fdl and fd2, (e.g. 103, 104) with distinct phase curvatures. The ability of 102 to produce two different co-propagating beams may be provided by incorporating a lens having multiple sections with different physical curvatures, or by incorporating a lens made of a birefringent material that has two different refractive indices, or by incorporating optical elements with lens properties due to geometric phase principles or other micro- or nano-structured patterns etched or deposited on a substrate. The two beams may also be generated by use of spatial light modulators or spherical mirrors with different curvatures in different parts of the mirror, or similar methods. The two co-propagating beams are directed to a recording device in a manner that allow them to produce an interference pattern 105, which is then recorded by an image recording device (not shown) and stored 106 for subsequent calculated reconstruction of the image 107 computed in a computing device 108. As noted above, multiple phase-shifted interference patterns (raw holograms) are recorded and stored for use in creating a complex hologram and calculated reconstructed images. The method of formation of the complex hologram and the reconstruction process are described in detail in the incorporated documents and are thus saved from detailed reiteration here. Briefly, the recorded holograms with different phase factors are super-imposed on each other in a computing device 108 by the following operation: )[exp(±i0n-1) - exp ( ± i0n+1)]; (equation 1) wherein HFis the complex hologram, H„ are the raw or recorded holograms (interference patterns), and n the index of the phase shift of a given raw hologram, with nmaxphase shifted images, and 6n-1= 9nmax, for n=l, and 0n+1= , for n=nmax. The complex hologram is then reconstructed into a 2D image s representing a single in-focus plane by one of a number of different computational operations. One common method is Fresnel Propagation, exemplified in the following equation:

[0011] (equation 2) wherein the asterisk represents a 2D convolution operation, zrecis the desired distance of the in-focus plane at which the hologram is to be reconstructed, and the term after the convolution operator represents the impulse response function (IRF) that describes propagation in space by a distance of zrec. In the IRF, the Amplitude term is a system dependent amplitude that can be chosen to impose desired characteristics in its Fourier transform, and the exponential term is a propagation phase function for optical propagation by a distance of zrec- Other image reconstruction methods may be applied, including angular spectrum reconstruction, image inversion, compressive sensing and deep learning computations, amongst others.

[0012] For example, an angular spectrum method may be employed in which the reconstruction is performed using an equation of the following general form: s x.y.Z gc) = F~ {F{HFx, y, zh)} x 0TF(x, y, zrec)} (equation 3)

[0013] Wherein F denotes the Fourier transform operation and F1denotes the inverse Fourier transform operation, and the OTF is the Fourier (frequency space) representation of the exponential term in equation 2, and has the following form: (equation 4)

[0014] In which kxand kyare frequency coordinates corresponding to the spatial coordinates of the hologram, and AOTF is an amplitude envelope which is typically 1 for frequencies with support in the reconstructed image and 0 for frequencies higher than that limit.

[0015] Once it is computed, the reconstructed image is then displayed on a computer monitor or other suitable display device. Note that equations 2 or 4, or another reconstruction operation, may be repeated many times for any different zrecas desired to create a three-dimensional collection of images.

[0016] FINCH imaging is also capable of optical super-resolution, in which objects that are close to each other may be resolved as separate objects in a FINCH image even though they are not resolved as separate objects in a standard (or "classical") image. Referring to Figure la and considering a single infinitesimally small object 111, classical optical imaging 110 simply requires a lens 112 to receive light from 111 and focus that light into an image 113, magnifying the object by the blurring function known as the pointspread function (PSF). A given conical angle of the light emitted from the object point 111, with a finite circular projection on the plane of the lens 112, is accepted by the lens. The accepted light beam, with radius 114 Rbeam, along with the distance 115 d, to the image plane, may be thought of as a lens with an effective numerical aperture NAbeam - Rbeam / d,, and the classical image spot size A, of the object point is inversely proportional to this effective NA. Referring to the representation 120 of FINCH imaging of a single infinitesimFal object 111 using a FINCH optical system 102 located the same distance away from the object 111 as a classical lens 112 shown in 110, the number and size of the fringes in the hologram 106 encode the depth of the object point being reconstructed, conferring on FINCH the ability to encode three-dimensional (3D) information. The self-interference of the light confers a super-resolution factor of up to twice the normal optical limit at any given wavelength by incorporating sample information in both light beams that interfere. That is, there are two signal beams rather than the individual signal and reference beams that are characteristic of classical holography. The largest increase in resolution occurs at the plane in which the two differentially focused beams have the same diameter. If a FINCH system is arranged so that the plane at which the hologram is recorded is at the distance 115 d, from the FINCH optical system, it has been shown (see Siegel, Rosen, and Brooker "Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy," Optics Express 2012 Volume 20 Issue 18 pages 19822-35 incorporated herein by reference in its entirety) that the resultant hologram has an effective NA (NAH) of its own, which is equal to NAbeam- Upon the reconstruction calculation in the computing device 108 by equation 2 or other methods, the final spot size of the FINCH image 121 is thus inversely proportional to twice the NAbeam, leaving it as half the width of the classically imaged spot. Since the lateral magnification of FINCH is the same at any distance from the optical system as that in classical imaging, this results in the lateral resolution of FINCH being twice that of classical imaging in this optimal arrangement. This is further illustrated in another classical imaging diagram 130, in which the classical lens 112 cannot use the light received from a pair 131 of closely spaced object points to create a classical image 132 that resolves (separates) the images of the two points in the pair 131. In diagram 140, depicting a FINCH system 102 imaging the same pair of points 131, the recorded hologram 141 is processed by the computing device 108 to an image 142 that does resolve the pair of points as separate from each other, showing that FINCH does not adhere to the classical Lagrange invariant that describes lateral magnification in classical optical systems in which angular magnification and lateral magnification change equivalently to one another. FINCH violates the classical Lagrange invariant and thus improves both single and two-point lateral resolution by a factor of up to 2 by allowing the lateral magnification to decrease by up to 50% while maintaining the same angular magnification.

[0017] An example embodiment of a state-of-the-art FINCH optical system as in "Single shot holographic super-resolution microscopy" is illustrated in Figure 2. In Figure 2, incoming light 201 from an object is linearly polarized at an input polarizer 202 and passed through the birefringent lens assembly 203 such as, for example, in US patents 10,228,655, 10,289,070, 10,423,123, and 10,591,870 and patent application 20170185036, and "High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers," Nature Photonics, 10(12), 802-808 2016.. The polarization orientations of 202 and 203 are arranged so that after passing through 202, the light is polarized at +45° and -45° relative to the ordinary and extraordinary refractive indices of the birefringent optics in 203. The birefringent lens assembly 203 includes at least one birefringent lens as well as any other optics necessary to transform the beam, standard converging or diverging lenses, birefringent compensating optics, and any other optics necessary to achieve the interference of the beams. The birefringent optical assembly thus separates the incoming beam into two outgoing beams, polarized along the ordinary and extraordinary refractive indices, each with its own phase curvature that is a function of the incoming phase curvature and the birefringent lens curvature and respective refractive index. Following 203, a quarter-wave plate 204 is placed in the beam path, with its slow axis aligned ±45 degrees to the ordinary and extraordinary axes of the birefringent lens. This has the effect of turning the linearly polarized light from the birefringent lens into circularly polarized light, one beam with right-handed circular polarization and one with left-handed circular polarization. This waveplate may be a broadband waveplate that applies the same quarter-wave phase shift to every incoming wavelength over its range and does not need to be calibrated. The two circularly polarized beams may be brought to interfere by passing them through an array 206 of differentially aligned micropolarizers of varying polarization orientations 207, 208, 209, 210 overlaying the image sensor at interference detection plane 205 wherein each micropolarizer is of the size of one of the detector pixels and is registered to a specific detector pixel. The angles of the polarizer transmission axes of the micropolarizers with respect to the waveplate slow axis controls the phase of the interference between the two beams recorded at the detector pixel registered to each micropolarizer. Multiple phase shifted holograms may then be recorded simultaneously, interspersed with each other over the entire array of pixels. For example, in one embodiment, the micropolarizer array may contain micropolarizers with transmission axis orientation of 0°, 90°, 180°, and 270° (or -90°) with respect to the quarter wave plate, resulting in the collection of multiple phase shifted raw holograms with relative phase shifts of 0, n / 2, n, and 3n / 2 radians (or 0°, 90°, 180°, and 270°). The micropolarizers may be of any convenient set of axis orientations to produce multiple holograms with any desired set of relative phase shifts. Following the recording of the raw holograms, the different phase shifted holograms may be separated from each other in the computing device. This results in a set of holograms, each of which has a quantity of blank pixels equal to (device pixel count)*(n-l) / n, where n is the number of phase shifts used. Figure 3 illustrates an exemplary embodiment of separating multiple individual phases of a hologram from an interspersed hologram recorded on a micropolarizer camera. The recorded hologram 301, which is the result of recording an interference pattern with the embodiment of Figure 2, possess a set of four holograms of different phases, each recorded by a quarter of the pixels overlaid with a particular micropolarizer orientation such as 0°, 90°, 180°, or 270° as discussed above, and interspersed with each other over the entire array of pixels. The different phases are, in a computing device 302, de-interspersed from each other and thereby abstracted from the recorded hologram into independent holograms 303-306. The computing device 302 may be identical with the computing device 108 that produces the reconstructed image of the object, or else 302 may be a separate computing device, including a computing device embedded in the camera that records the interspersed hologram. Immediately after being deinterspersed, each of the four holograms 303-306 as noted above possesses significant data on the % of its pixels that have one micropolarizer orientation, while possessing no data on the % of the pixels that have the other three micropolarizer orientation. For example, in the de-interspersed hologram 303 that contains data from the set of pixels with the 0° micropolarizer orientation, the pixels that have the 90°, 180°, or 270° micropolarizer orientations are assigned a value of zero since the 0° interference data was not recorded on those pixels. The case is likewise for the 90°, 180°, and 270° orientations contained in 304-306. The pixels in each de-interspersed hologram that are assigned a value of 0 are called blank pixels. These pixels, or the blank pixels of any similarly obtained set of interspersed holograms or images, may be reassigned with values calculated by nearest neighbor or other interpolation methods, to maintain the sampling interval of the imaging device. A recentering operation of single-pixel shifting the interpolated data may optionally be performed in order to improve the overlap of the raw holograms. Alternatively, the blank pixels may be removed and the sampling interval of the image data increased by a factor appropriate to the number of phase shifts recorded. For example, if four phase shifted raw holograms were recorded on a sensor of the type described in the current embodiment of 2048x2048 pixels of 5 micron pitch, each raw hologram would have (2048*2048)*(4-l) / 4 = 3,145,728 blank pixels. These pixels could be filled with interpolated data, or simply be removed, with a concomitant reassignment of the sampling pitch to 10 microns. The resultant holograms from any of these methods are referred to as the "filled-in" holograms 307-310. In any of these cases, the individual filled-in phase shifted holograms may then be combined into a complex hologram with magnitude 311 and intensity 312 as described above and in the incorporated literature, and then processed further in a computing device 108 to produce the reconstructed image 107 of the object recorded in the hologram 301.

[0018] One topic of intense interest for the application of FINCH imaging technology is microscopy, including research, clinical and metrology microscopy. A microscope was constructed to incorporate the FINCH technology described earlier herein into a hybrid microscope that can record widefield, confocal, FINCH and confocal FINCH images or holograms under either fluorescence excitation, reflected light, or transmitted light illumination. The microscope can also create any of these types of images from luminescence light that occurs independent of an electromagnetic light source. Briefly, referring to the microscope schematic 400 in Figure 4 and omitting mirrors and other elements that do not contribute focal power or affect the FINCH holographic process, a microscope objective lens 402 is the first lens in the FINCH microscope that images a specimen (Sample) 401. A 4F relay consisting of lenses 403 and 404 is placed to transfer the image of the back pupil of the objective 402 onto a birefringent lens (BRL) assembly 203 that produces the differentially focused beams necessary to achieve FINCH interference. As in any modern microscope with infinity corrected optics, the space between lens 404 and the BRL assembly 203 is infinity space for insertion of standard microscope dichroic beam splitting filters 405 and any other optic such as emission filters 413 and polarization optics. Prior to 203 is a linearly polarizing beam splitter (PBS) 406 that transmits light polarized midway between the BRL birefringent axes. The rejected polarization from the PBS 406 is directed to a standard microscope tube lens 407 and focused onto a standard camera 408 such as CCD or CMOS to capture a widefield or confocal image for the purpose of comparison to the FINCH or CINCH image. This comparison widefield or confocal image is not a strict requirement of FINCH imaging and is used here solely as a benchmark comparison so that an identical widefield or confocal image can be compared to the FINCH or CINCH (confocal FINCH) image. In some cases a FINCH imaging system is attached to an emission port of a standard microscope and a camera attached to another camera port of the microscope to obtain a widefield image.

[0019] Returning to the FINCH optical path, positioned after the birefringent lens assembly 203 is an achromatic quarter-wave-plate (QWP) 409 with its slow axis aligned midway between the birefringence axes of the BRL. As noted above for the QWP 204, the QWP 409 converts the orthogonally linearly polarized light beams 103, 104 that it receives into orthogonally circularly polarized light beams, still with differing focal lengths, that are caused to interfere at the micro-polarizer camera 206. The beams 103, 104 are both defocused beams of light from the microscopic sample. In the microscope that was constructed, the achromatic QWP is used to extend the useful working spectral range to cover most of the interesting biological fluorescence emission wavelengths. Confocality of imaging is provided by a spinning Nipkow pinhole disk 410 (US Patent 11,029,646 issued June 8, 2021) that can be inserted into the optical path at the focal plane between 403 and 404, if desired. Fluorescence and reflectance illumination light is provided from illumination lamp 411, while transmitted illumination light is provided by illumination lamp 412.

[0020] To capture a widefield or confocal standard or FINCH image with the microscope described in 400, the operating procedure of the microscope is identical to that of a standard widefield or spinning disk confocal microscope. The sample is brought into focus, the exposure time is metered to maximize the signal-to-noise ratio while avoiding saturation, and a single exposure is captured. Following a single image capture, the recorded hologram is converted to a complex hologram as in Equation 1 and related discussion, reconstructed by Fresnel Propagation as in Equation 2 either directly to the focal plane of the objective, or alternately into a calculated stack of reconstructed images representing a through-focus series of planes. The reconstructed focal plane image can be displayed live during image capture, if desired. The absolute value of the reconstructed image was used for further analysis. Deconvolution of the reconstructed image or image stack was performed using a custom FINCH PSF and a blind deconvolution with entropy regularization.

[0021] BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 (Prior Art) illustrates a generalized FINCH imaging system according to some embodiments. Figure 1A (Prior Art) llustrates example imaging of a single infinitesimally small object by classical optical imaging or by FINCH imaging according to some embodiments.

[0023] Figure 2 (Prior Art) illustrates a FINCH optical system as in "Single shot holographic super-resolution microscopy" according to some embodiments.

[0024] Figure 3 illustrates separating multiple individual phases of a hologram from an interspersed hologram recorded on a micropolarizer camera according to some embodiments.

[0025] Figure 4 illustrates a generalized view of an example FINCH system, according to some embodiments.

[0026] Figure 5 illustrates an expanded set of idealized FINCH PSFs to exemplify the characteristics expected of a FINCH hologram PSF under idealized conditions in accordance with some embodiments.

[0027] Figure 5A illustrates a modified concept of FINCH hologram formation process with interference of two beams of non-identical intensity according to some embodiments.

[0028] Figure 5B illustrates a modified concept of FINCH hologram formation process with interference of two beams of non-identical intensity and imperfect centration according to some embodiments.

[0029] Figure 6 illustrates a sample of fluorescent beads imaged at an emission wavelength by FINCH microscopy on a microscope of the type shown in Figure 4, according to some embodiments.

[0030] Figure 7 illustrates FINCH images of the same beads as shown in Figure 6, on a microscope of the type shown in Figure 4, with a confocal spinning disk placed in and the optical path as shown in Figure 4.

[0031] Figure 8 illustrates a collimated laser beam being introduced to the microscope at a position that bypasses all the microscope optics other than the FINCH optics, according to some embodiments.

[0032] Figure 9 illustrates an optical arrangement used to test whether the image relay composed of two lenses causes any aberrations in the FINCH holograms, according to some embodiments.

[0033] Figure 10 illustrates an optical arrangement used to testthe performance of the remainder of optics (other than the objective) in a microscope incorporating FINCH optical system optics, according to some embodiments.

[0034] Figure 11 illustrates the point spread function (PSF) holograms taken with various versions of configurations shown in Figures 8, 9 and 10, from a collimated laser used to simulate a perfectly expected beam from an objective. Figure 12 illustrates an optical arrangement in which a collimated laser is used to back-illuminate a pinhole at the focus of an objective to provide a pinhole back-illuminated with a perfect beam, according to some embodiments.

[0035] Figure 13 illustrates the results when the pinhole shown in Figure 12 is imaged with FINCH in widefield and spatially filtered mode in which a spinning disk was inserted at the intermediate image plane between relay lenses, but in which the illumination light did not pass through the spinning disk, according to some embodiments.

[0036] Figure 14 is a set of widefield and spatially filtered fluorescent images taken in an optical arrangement with a different objective lens, according to some embodiments.

[0037] Figure 15 illustrates that in general with FINCH optics, the birefringent lens produces two beams with different focal lengths and the hologram is recorded at a location in which the first beam is in a diverging defocus range, whereas the second beam is in a converging defocus range, at which location both beams are the same size so that the overlap of the beams is maximized.

[0038] Figure 16 illustrates the results of the FINCH imaging of 200 nm point spread function (PSF) beads with a 40x Zeiss objective on a Zeiss microscope, comparing the appearances of the interfering beams at a FINCH camera and the out-of-focus standard images taken by moving a widefield camera back and forth relative to the standard lens focal plane, according to some embodiments.

[0039] Figure 17 illustrates a similar data set as Figure 16 using the same microscope and methods that produced Figure 16 but obtained using a different objective, according to some embodiments.

[0040] Figure 18 illustrates in a consistent format the evolution of the idealized concept of FINCH microscope image formation through the observations of FINCH holography with a perfect laser beam as a real world model of an idealized depiction of FINCH images, and progresses through the introduction of a microscope objective that induces aberrations in the laser beam that are corrected by spatially filtering.

[0041] Figure 19 illustrates a continuation of the summary of Figure 18 by showing that it is possible for different objectives to produce markedly different beams that then are processed by the FINCH optics to produce either excellent holographic data or significantly aberrated holographic data.

[0042] Figure 20 illustrates widefield and FINCH data of a microtubule sample, in accordance with some embodiments. Figure 21 illustrates widefield and FINCH images of a different microtubule cell from the same slide as used in Figure 20.

[0043] Figure 22 illustrates the two FINCH beams in a FINCH system, tracing them from the light received from the object through the creation of the beams that create independent images, in accordance with some embodiments.

[0044] Figure 23 illustrates an aberration may be introduced at the first lens in the system, the objective lens, according to some embodiments.

[0045] Figure 24 illustrates a scenario in which the primary lens is not aberrated but a tip / tilt aberration in the birefringent lens causes the two beams to propagate away from the birefringent lens with different wave vectors, in accordance with some embodiments.

[0046] Figure 25 illustrates a double-telecentric lens system including telecentric optics, according to some embodiments.

[0047] Figure 26 illustrates a birefringent lens that can be placed at the location of a telecentric stop, according to some embodiments.

[0048] Figure 27 illustrates through-focus spot diagrams of two objective lenses and also corresponding Seidel diagrams showing the Seidel coefficients of the spherical aberration of all the lens components in some example embodiments, in a graphical format.

[0049] Figure 28 illustrates the effect of one corrective strategy, adding an aspheric lens to fix the spherical aberration, according to some embodiments.

[0050] DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0051] In recording holograms and producing images with multiple FINCH microscopes of the type of 400, the current inventors have observed that there can be significant discrepancies between the idealized picture of hologram formation as described above and the observed holograms actually obtained from real microscopic specimens. In many instances the discrepancies were analyzed by imaging sub-resolution size fluorescent beads with the microscopes, in order to visualize, using the simplest possible sample, the true nature of the point-spread function (PSF) of the FINCH microscope systems, from the creation of the raw holograms as recorded on the camera, to the complex hologram deduced from the raw holograms, to the finished reconstructed image created from the complex hologram. Most prominent of the discrepancies are complex holograms with significantly highly contrasting structure in amplitude and deviations from spherical quadratic slope in the phase terms, which is associated with a reconstructed image PSF with significant side-lobes or shadows. In more complicated samples the discrepancies can manifest as large shadows around objects or even contrast reversal in which parts of the image that should be dark are bright and vice versa.

[0052] In Figure 5 there is an expanded set of idealized FINCH PSFs to exemplify the characteristics expected of a FINCH hologram PSF under idealized conditions. Figure 5 contains simulated images of ideal FINCH PSF components, along with line profiles taken through the center of the PSF images, as indicated by the lines drawn through the images (see images 501, 503, 505-508, 513, 515, 517). The two separate beams that interfere (Beam 1 501 and Beam 2 503) are considered to have perfectly smooth Gaussian intensity profiles 502 and 504 that are identical to each other. Note that figure 5 displays a set of four phase shifted raw holograms 505-508, each of which is a spherically symmetrical set of rings obeying a Fresnel phase pattern, with 4 different phase offsets corresponding to the phase shifts of Phase 1 = 0°, Phase 2 = 90°, Phase 3 = 180°, and Phase 4 = 270°. Each raw hologram has its own maximum and minimum at differing spatial locations, and the phases separated by 90 degrees are the inverse of each other as can be seen easily in profile plots 509-512. When combined into the complex hologram 513 (intensity), 515 (phase) as by equation 1, this results in a complex PSF with a perfectly smooth Gaussian intensity envelope 514 and a phase term 516 that obeys a perfect spherical quadratic phase. When further processed into the reconstructed image 517 as by equation 2, the reconstructed PSF has a nearly Gaussian intensity 518 with essentially no sidelobes. For comparison, the image 519 and profile 520 of a standard (nonholographic) PSF is included as well. Note that the standard widefield PSF is wider than the FINCH reconstructed image PSF, showing the super-resolving nature of the FINCH technique.

[0053] Figures 5A and 5B contain modifications of Figure 5 to exemplify effects of discrepancies between Beams 1 and 2. The beams 531 and 533 have significantly different intensity profiles 532 and 534. The biggest difference is that Beam 2 has an intensity that falls toward zero much faster than Beam 1, so that even though the beams are still centered with respect to each other, the interference efficiency is no longer perfect. The results of this, shown in the raw holograms 535-538 and line profiles 539-542, show that the number of Fresnel rings in the raw hologram is reduced, and the relative intensities of the various rings in each raw hologram may be changed. This is manifest in the complex hologram intensity 543, 544 as an intensity that is different from either Beam 1 or Beam 2, although the complex phase 545, 546 shows little difference. The reconstructed image 547, 548 shows a slight widening and an increase in the sidelobe strength, both of which are undesirable.

[0054] Figure 5B contains a further modification to Figure 5A, namely an offset in center position of Beam 2 by about 5% of its diameter, toward the bottom right corner of the image, as indicated by the white arrow 581. This imperfect mutual centration means that the upper left section of Beam 1 and the lower right section of Beam 2, as indicated by the crescents 582, 583, no longer overlap any part of the other beam. This further leads to asymmetry in the raw holograms 565-568 which can be seen easily in the plot profiles 569-572 that show higher intensities on the right side of the holograms than on the left. This is manifest in the Complex hologram intensity 573, 574 showing an asymmetrical intensity; and in the complex hologram phase 575, 576 showing changes in the phase pattern as well as an apparent loss of phase data in the upper left and lower right sides of the pattern (indicated by crescents 584, 585), which correspond to the areas where Beam 1 and Beam 2 no longer overlap. In the reconstructed image 577, 578 a shift can be seen in the position of the image and peak of the profile as well as asymmetry in the profile, both of which are undesired.

[0055] Figures 5A and 5B demonstrate the effects of discrepancies from the idealized concept. A simple mismatch of beam intensity distributions, even though each is symmetrical and smooth on its own right, and a slight offset of the mutual center positions of the beams, is sufficient to noticeably affect the raw holograms and final reconstructed image. In a real imaging system such as a microscope, with a possibility of more significant aberrations and asymmetries in the individual Beams 1 and 2 that are defocused beams originating from the sample, the effects of imperfect beam matching could be significant.

[0056] In order to test whether the FINCH microscopes were performing as the idealized and modified FINCH PSFs In figures 5, 5A and 5B suggest, a sample of 200nm fluorescent beads was imaged at 590 nm emission wavelength by FINCH microscopy on a microscope of the type of 400, using a 60x Nikon 1.49 NA TIRF objective, the results of which are shown in Figure 6. These beads are on the order of the resolution limit of the microscope objective [Rayleigh limit: 0.61A. / NA = 242 nm; Abbe limit: 0.5A. / NA = 198 nm] and are thus a good choice for measuring the image PSFs. Each bead hologram and image shown should be considered as an instance of the type of PSF shown in Fig. 5. Images 601, 602 (corresponding to 501, 503 or 531, 533 or 561, 563) of each defocused isolated beam, Beam 1 and Beam 2, were recorded at the hologram plane, and then the four phase shifted holograms 603-606 (corresponding to 505-508 or 535- 538 or 565-568) were recorded and processed by equations 1 and 2. A whole field of view corresponding to the hologram camera chip dimensions was recorded but only a small cropped section is shown for the sake of clarity. Note that the two beams produce defocused images 601, 602 that are quite dissimilar to each other. This difference suggests that the discrepancy discussed earlier is already present in the individual defocused beams before the FINCH interference process even begins. Once the interference is recorded as in the raw holograms, it can easily be seen that the raw holograms 603-606 have extra undesired structure beyond an ideal Fresnel profile, including always having a small feature in the middle of the hologram. These characteristics are carried forward into the complex hologram, which shows significant structure in the magnitude 607 (corresponding to 513 or 543 or 573) that differs from an ideal smooth profile, and in the complex phase 608 (corresponding to 515 or 545 or 575) in which transitions between wrapped portions of the phase are not sharp, and in which there is always a flat or soft feature in the middle. In the reconstructed image 609 (corresponding to 517 or 547 or 577) and the profile 610 (through the bead indicated with the line in image 609) (corresponding to 518 or 548 or 578) can be seen an image spot PSF with a large halo (sidelobe) and shadow around it, in which the halo intensity is about 10% of the intensity of the image peak as seen at the x-axis positions of ca. 20 and ca. 50 in the plot 610. This halo, which is a full or partial ring of intensity around the central intensity of an image point, is an exemplar of the type of discrepancy referred to earlier and which it is the goal of these teachings to eliminate. The full or partial ring of darkness between the central intensity of an image point and a halo is referred to herein as a shadow.

[0057] Many different attempts have been made to eliminate these halos by a variety of means, including optimizing the optical alignment and illumination; optimizing the sample stability; optimizing lens quality of the FINCH optical system; and reducing noise in the image recording process. None of these optimizations has eliminated the halos. The one item that has eliminated halos is the use of a confocal spinning disk 410 in the intermediate image plane of the FINCH microscope 400. Figure 7, contains FINCH images of exactly the same beads as shown in Figure 6, with the only change being that confocal spinning disk 410 was placed in between lenses 403 and 404 as shown in Figure 4. The confocal images of the 200 nm bead PSF models show individual Beam 1 and Beam 2 images 701, 702 that are nearly featureless and which have a much more ideal intensity profile. All four phases 703-706 of the raw hologram also keep an ideal appearance and profile quite similar to the ideal ones 505-508 shown in Figure 5, with none of the extraneous features in the middle of the hologram seen in 603-606. The complex magnitude 707 of any single bead is also featureless, smooth and ideal (with the minor exception of imaging noise); the complex phase 708 is an ideal spherical quadratic phase with sharp wrapping transitions and no softness or flatness in the middle. Further, the reconstructed image 709 does not show shadows or halos, which is confirmed by the plot profile 710 taken through the bead indicated by the line in image 709. Note that the linear interference structures in 707 (top right and middle left) are simply due to two beads located close to one another and that the reconstructed images of the beads from those parts of the hologram are resolved without halos in 709. Thus it seems that the discrepancy is already present in the beam prior to the image relay; therefore it must arise either in the sample 401, objective 402, or LI 403. As the most complicated element in the microscope, the objective 402 including its interface with the sample 401 is the most likely candidate for the source of the discrepancy; however it is necessary to confirm this and test the strength of the effect of the objective on aberrations in the hologram.

[0058] Following these observations, it is necessary to understand what is the cause of the improvement in the confocal FINCH hologram PSFs as compared to the widefield FINCH hologram PSFs. The isolation (by the spinning disk) of the imaging volume to a small volume around the focal plane is the most obvious candidate; however the beads themselves are already smaller than the confocal image axial focal range that is greater than 500 nm and the confocal isolation has no rational ability to confine the image volume to be smaller than the beads. If the confocality is not able to improve the hologram PSFs, then another process must be occurring. The current inventors have found that the reparative process is in fact spatial- domain spatial filtering of the image beams by the spinning disk. The pinholes in the disk are by design slightly larger than the Airy disk size of the beams at the location of the disk, which is the ideal size for performing spatial filtering. The Airy disk is known to one skilled in the art as the size of the focal spot of a beam from its peak to the first intensity minimum. In this conceptualization, the beam of light coming from the sample through the objective is considered as if it was a laser beam with aberrations and structure in it (such as those contained in non-TEM00 modes, as known to one skilled in the art), which is then focused down onto the spinning disk pinholes to spatially filter it and remove the aberrations and pass only the TEM00 mode. Note that this conceptualization does not require true confocality (i.e. the illumination does not need to pass through the disk, only the emitted light from the object does) so further demonstration of similar improvement in spatially filtered FINCH holography is required to confirm this understanding.

[0059] A comprehensive series of measurements was made in order to conclusively determine whence arises the discrepancy, and whether spatial filtering alone can fix it without requiring true confocality, and furthermore to determine if there are other ways to remove the discrepancy.

[0060] First, we define three alternate configurations (800, 900, 1000) of the microscope 400, as shown in Figures 8, 9 and 10 respectively. All of these configurations were for the purpose of introducing a collimated single-mode laser beam (indicated by the wide beams output by the Gaussian laser 802 in each configuration) into various parts of the FINCH microscope in order to test the performance of all the optical components and determine if any of the components introduced aberrations into an otherwise perfect beam. A collimated single-mode laser is a perfect non-aberrated optical beam and therefore should produce the most ideal hologram PSFs possible. Essentially it is supposed to stand in for the light beam obtained from a microscope infinity corrected objective, that should be a plane wave when the object is at focus. The version of 400 that served as the basis for 800, 900 and 1000 is a Nikon Eclipse microscope containing the objective 402 and first relay lens 403, with all items from the spinning disk until the cameras being part of a custom assembly with the following components: (410 CellOptic custom spinning disk with 50 |im pinholes; 404 relay lens 2 = 150 mm 2" achromat from Thorlabs; 413 microscopy emission filters from Chroma or Semrock; 406 polarizing beamsplitter from Thorlabs; 203 custom Birefringent lens and compensating plate from CellOptic, BBO with -457 mm PCV curvature coupled with 200 mm achromatic lens from Thorlabs; 409 broadband QWP from Thorlabs; 206 polarization camera from FLIR).

[0061] Configuration 800 (Figure 8) depicts the collimated laser beam 802 being introduced to the microscope at a position 801 that bypasses all the microscope optics except leaving the FINCH optics: the polarizing beam splitter, the birefringent lens, the quarter wave plate and the camera. The components 404, 405, 413 were removed 804. There is an adjustable iris 803 at the laser collimator to control the beam width. Four different beam widths were recorded with consistent results, but only the 12 mm beam width results will be presented later herein. This configuration is to test the isolated performance of the FINCH optics.

[0062] Configuration 900 (Figure 9) was used to test whether the image relay composed of 403 and 404 causes any aberrations in the FINCH holograms. The laser light was introduced to the FINCH optics by first going through a relay system similar to that in the FINCH microscope 400 (which reduces the beam width). Configuration 900 depicts the collimated laser beam 802 being introduced to the microscope through an optical relay of the type shown in 400 with lenses 901 (an independent 200 mm focal length tube lens) standing in for 403 and 404 (a 2" 150 mm focal length achromat lens, reintroduced 902 in its standard location) but without using the built-in tube lens of the Nikon Eclipse microscope before passing to the FINCH optics: the polarizing beam splitter, the birefringent lens, the quarter wave plate and the camera. The components 405, 413 were removed 903. There is an adjustable iris 803 at the laser collimator to control the beam width. Four different beam widths were recorded with consistent results, but only the 12 mm beam width results will be presented later herein. Configuration 1000 (Figure 10) was used to test the performance of the remainder of optics incorporated in the Nikon Eclipse microscope based FINCH optical system optics (other than the objective) including the built-in Nikon tube lens as well as the confocal disk, and excitation / emission dichroic and emission filter. Configuration 1000 depicts the collimated laser beam being introduced to the microscope through all of the optics of the Nikon Eclipse microscope based FINCH optical system except the objective 402. The dichroic and emission filters (405, 413) and spinning disk (410) were alternately inserted into and removed from (1001, 1002) the optical path. There is an adjustable iris at the laser collimator to control the beam width. Four different beam widths were recorded with consistent results, but only the 12 mm beam width results will be presented later herein.

[0063] A common measure of beam quality is its intensity profile, which is the variation in intensity from the center of the beam to its outermost edge (radial extent). One beam profile that is often considered to be ideal is a Gaussian profile, known to one skilled in the art as an intensity that decreases smoothly from the center to the radial extent of a beam according to the Gaussian equation of the form l(x)=a*exp(x2 / 2o2), wherein I is the intensity at radial location x, a is a scaling constant, and o is a term that describes the width of the beam. A Gaussian beam may also be referred to as a TEM00mode beam, as known to one skilled in the art. For the teachings herein, a perfect or ideal beam is one that possesses a smoothly and gradually varying and radially symmetric intensity profile, without strong or sharp variations of intensity which can collectively be referred to as "structure". A further consideration for FINCH is that for ideal holograms to be formed, each of the defocused beams used to create the hologram should be ideal. Ideal FINCH raw holograms of PSF objects have intensity profiles that are the magnitudes of Fresnel phase patterns as depicted in 505, 506, 507, 508 and as described in US Patent No. 8,179,578, "Digitally spatially incoherent Fresnel holography." The ideal complex hologram derived from ideal raw holograms should have a magnitude that is similar to the intensity profiles of the beams that were interfered term (similar to the relationship of 513 to 501 and 503), without large amounts of structure in the intensity, and should have a phase term that is closely approximated by a wrapped quadratic function as in 515. To approach this quality in practice, a perfectly collimated Gaussian laser beam without defects or aberrations can be used with FINCH optics to create a FINCH hologram from the interference of two distinct beams created from the single laser beam received by the FINCH optics, at any plane after the creation of the two beams.

[0064] Defects and aberrations that are sometimes observed in defocused optical beams include but are not limited to uneven intensity profiles, the presence of optical speckle, other randomly located patterns or dark spots in the beam, and diffraction or other interference patterns in the beam. Defects or aberrations in optical beams can be a result of the propagation of multiple wave modes propagating within the beam other than the Gaussian mode. Defects and aberrations in focused images can include halo / shadow patterns as described previously herein, as well as all of the optical aberrations known to one skilled in the art as Defocus, Spherical Aberration, Coma, Astigmatism, Field Curvature, and Distortion. Many of the aberrations of focused images are described by Zernike's polynomials, which is a set of equations that also defines some other aberrations that are incorporated into the set of aberrations that can be corrected by the teachings herein. Any beam or image may contain any number of aberrations, of which some or all are corrected by the teachings or embodiments herein. Similarly to the teachings above regarding the use of spatial filtering to removed unwanted features and aberrations from light beams, there are other methods for removing defects and aberrations form beams and images, and these methods can also be termed as correcting aberrations or defects. Beams and images that are corrected in this way may be referred to as corrected images, or restored images, where the restoration is to a state that is as if the beams or images were perfect and non-aberrated. If an appropriate correction is applied to defective or aberrated light beams or other electromagnetic waves received from sample objects, it is possible to create holograms from said objects that are as perfect or ideal as if the waves from the object had actually originated form a perfectly collimated and non-aberrated laser beam.

[0065] The PSF holograms taken with various versions of configurations 800, 900 and 1000 from the collimated laser to simulate a perfectly expected beam from an objective are shown in Figure 11. In brief, all of the PSF holograms shown are of excellent quality with no notable defects or aberrations when they were recorded. The isolated Beam 1 and Beam 2 intensities are smooth, relatively featureless and similar to each other, with no random, asymmetric, or sharp intensity variations. The raw holograms are all ideal in their appearance, being similar to 505, 506, 507, 508, and the Magnitude and Phase of the complex holograms are ideal by being similar to the intensities of the interfering beams and being approximated by a wrapped quadratic function, respectively. The reconstructed images all show no halo or shadow. The conclusion to draw from this is that since all these configurations produced ideal hologram PSFs when they operated on an ideal beam of light, these components are not the source of the discrepancy seen with light coming from an objective focused on a point source: The relay lenses, spinning disk, dichroic and filter, polarizing beam splitter, birefringent lens, quarter wave plate and camera are not responsible for any aberrations. Next, we examined the system when used with a microscope objective focused on a point source. As shown in Figure 12, the collimated laser was used to back-illuminate a l um pinhole at the focus of a lOx 0.3 NA Nikon Plan Fluor objective. A pinhole back-illuminated with a perfect beam, such as this, is a good stand-in for a microscopic specimen emitting light and can be used to assess the PSF image quality of a microscope objective. The pinhole was imaged with FINCH in widefield and spatially filtered mode, where spatially filtered mode means that the spinning disk was inserted at the intermediate image plane between 403 and 404, but the illumination light did not pass through it. The results are shown in Figure 13. In widefield, the fdl and fd2 beams are both heavily aberrated and significantly different from each other. These factors cause significant aberrations in the raw holograms, and defects in the center of the complex hologram. The reconstructed image shows significant halos of ca. 10% the maximum intensity as shown in the profile plot. That is, in widefield mode, the Beams, raw holograms and complex hologram are all aberrated, and there is significant halo (sidelobes) in the reconstructed image. In spatial filter mode, the fdl and fd2 beams are not aberrated and are very similar to each other. As a result, the raw and complex holograms are much better for the spatially filtered images in the bottom row of Fig. 13, and the reconstructed image for the spatially filtered has no halos around it. That is, in spatially filtered mode (with the spinning disk only in the imaging beam), the structure and aberrations in the Beams, raw holograms and complex hologram are all eliminated, and the reconstructed image is free of significant halo. From this we draw the conclusions that the objective introduced some aberrations, and the spatial filtering approach removed them without requiring confocality (because only the emission was spatially filtered).

[0066] Figure 14 is a similar set of widefield and spatially filtered fluorescent images taken with the Nikon 60x TIRF objective and 200 nm fluorescent beads. Images of single beads were cropped and examined as representative PSFs. The results show that without spatial filtering Beams 1 and 2 are compromised and the holograms are defective. As in Figure 13, spatial filtering restored the holograms and provided good results. Thus spatial filtering works to correct, to a more ideal state, actual aberrated fluorescence images from objectives and not just on model objects such as the 1 um pinhole or a collimated laser beam.

[0067] Considering that the objective seems to be the only significant source of aberration found in the hologram, it is worth considering whether all objectives show this extent of aberration or whether certain objectives show more, less or no aberration. If we could find differences between different classes of objectives, it would provide the impetus for the design of objective systems that work best with FINCH holographic microscopy. In our work we found that there is considerable variability in microscope objectives in terms of aberrations when examined at their design specifications for the defocus beam shape away from the focused image. This is the case experimentally and in computer design simulations of objectives. It is also well known that there are a wide variability in the degree of aberrations in microscope objectives (Jan Barghaan and Lauren Alvarenga, "This is not a Fishing Lure", Imaging and Microscopy pp 12-13, Vol 24 September 2022) at focus and all of this can be controlled by design parameters using computer driven optical design software such as Zemax. They state, "From a design and manufacturing perspective, however, the objective is the most difficult microscope component to produce. Plus, traditional design methods for objectives often lead to trade-offs in optical performance. While it is possible to make improvements for one key parameter of imaging, a compromise in another parameter is often necessary to accommodate this adjustment."

[0068] A further instrument was used to test the effect of different objective lens types on FINCH performance: A microscope of the general format of 400 was constructed using a Zeiss Axio Observer microscope to hold the objective lens and tube lens (since Zeiss infinity corrected microscope objectives are designed to work in Zeiss microscopes that have a 164.5 mm tube lens compared to Nikon objectives designed to work in Nikon microscopes with a 200 mm tube lens)(relay lens 1, 403) and a a 250 mm 2" achromat lens as relay lens 2 (404). This microscope is otherwise similar in design to the FINCH microscope based on the Nikon microscope frame. Two objectives were used: a Zeiss 40x Fluar 1.3 NA oil objective, and a Zeiss lOOx 1.3 NA Fluar oil objective. The 40x objective has fewer optical elements and corrections than the 60x TIRF objective and thus is a way to interrogate whether FINCH microscopy might benefit from less-corrected objectives that create less structure in the beams they create from light received from the sample. The lOOx objective is the same design class as the 40x but is of higher magnification, which necessarily requires more correction in the lens and is thus a test of differing levels of correction within a particular lens class. Similar to the imaging of 200 nm beads with the Nikon Eclipse based microscope, isolated images of Beams 1 and 2 were recorded through the FINCH optics as well as raw holograms that were processed into complex holograms and reconstructed images.

[0069] At the same time that holograms of beads were processed, as a further check to make sure that discrepancies between Beams 1 and 2 were not caused by the FINCH optics and instead are due only to the microscope objective, defocus images were also recorded on the pristine unmodified Zeiss microscope optical path using only original optics, to show that the widefield beam also presents different appearances at differing defocus ranges. The built-in trinocular port of the AxioObserver was used to record the widefield beam produced by the objective, without any effect of FINCH optics, at different defocus positions. Referring to Figure 15, it is seen that in general with FINCH optics, the BRL produces two beams with different focal lengths. The hologram is recorded at a location in which Beam 1 is in a diverging defocus range, whereas Beam 2 is in a converging defocus range, at which location both Beams are the same size so that the overlap of the Beams is maximized. A standard lens (as in the unmodified microscope widefield optical path), on the other hand, only produces an image at a single focal length, and to approximate the position of the hologram camera relative to the focal lengths of FINCH Beams 1 and 2, it is necessary to move the camera to measure the defocused beams at diverging or converging positions. Moving the sample closer to and further away from the lens is a very similar operation but not identical. Considering the standard optical path on the Zeiss microscope trinocular port, the camera is moved further away from the standard microscope tube lens to record the defocus beam as it diverges from focus, and is moved closer to the tube lens to record the defocus beam as it is still converging toward focus.

[0070] The results of the FINCH imaging of 200 nm PSF beads with the 40x Zeiss objective on the Zeiss microscope and of moving a widefield camera back and forth relative to the standard lens focal plane are shown in Figure 16. The widefield defocused images were collected on the unaltered trinocular port of the Zeiss Axio Observer microscope. The top row of FINCH images shows the isolated Beam 1 and 2 recorded on the FINCH camera, while the bottom pair of images comes from moving the camera to defocus positions on the trinocular port approximately 5 mm to either side of the focal plane. The sample was the same type of 200 nm fluorescent sample used for the FINCH images. A general similarity between FINCH Beams 1 and 2 and the widefield defocus beam images is observed, namely that there is some asymmetry between the defocus widefield beam images, though it is the same type as seen in the FINCH Beams 1 and 2. This is a confirmation that the differences in the Beams are not caused by the FINCH optics but are native to the objective lens itself. The FINCH raw hologram and reconstructed data are of significantly higher quality than the corresponding widefield (non-spatially filtered) FINCH data taken with the Nikon 60x TIRF objective (Figure 14 top row). The raw holograms taken with the 40x Zeiss objective show markedly fewer aberrations at all stages, from the raw hologram to the reconstructed image, and in fact show no halo (sidelobes) at all. This data confirms that appropriate design of an objective can significantly improve FINCH imaging performance. A similar data set is shown in Figure 17 for a lOOx Zeiss Fluar 1.3 NA objective using the same microscope and methods that produced Figure 16. However, there are more differences between the Beam 1 and Beam 2, which result in greater halos (sidelobes) in the reconstructed image spot. This is also apparent in the diverging and converging defocused widefield beams, which are more different from each other than the two widefield defocus beams from the 40x objective data in Figure 16. However, spatial filtering with the disk of the lOOx Zeiss Fluar 1.3 NA objective restores performance to those ideally expected as shown in the second row of Figure 17. In Figure 17 it is also demonstrated that spatial filtering also works well with this Zeiss objective to improve the FINCH image, showing that spatial filtering is applicable to other objectives besides Nikon objectives.

[0071] SUMMARY OF ANALYSIS OF BEAM QUALITY AND ABERRATIONS IN FINCH MICROSCOPY

[0072] The above-mentioned pattern of findings and teachings can be summarized with reference to Figures 18 and 19. Figure 18 displays in a consistent format the evolution of the idealized concept of FINCH microscope image formation through the observations of FINCH holography with a perfect laser beam as an idealized real world model, and progresses through the introduction of a microscope objective that induces aberrations in the laser beam that are corrected by spatially filtering. In the first row of Figure 18 is the ideal theoretical performance of FINCH imaging on an idealized Gaussian beam with no aberrations. The individual Beams have identical intensities and none of the structure such as rings or intensity variations that comes from optical aberrations, and they produce Raw holograms with neat circular Fresnel fringes, leading to a complex hologram with structureless Gaussian intensity and quadratic phase with sharp phase wrapping regions and a Reconstructed image with no halo. The second row shows a real FINCH optical system operating on a single mode laser that is as close as possible to a Gaussian intensity. The individual Beams are very similar to each other with little structure, resulting in Raw holograms that nearly match those in the theoretical data from the top row, along with a complex hologram with intensity with little structure and a quadratic phase, and a reconstructed image with no halos. The third row shows that the introduction of a microscope objective into the laser beam causes significant aberrations and structure in the individual Beams, which is carried forward into the raw and complex holograms as visible defects and significant halo in the reconstructed image. Removal of the defects by the spatial filtering procedure as in the bottom row is shown to remove the defects and return the hologram data to an ideal state with no obvious defects, little structure in the complex intensity, a quadratic phase and a reconstructed image without halo. The central point of Figure 18 is that the current state of the art FINCH optics are able to match the theoretical predictions regarding FINCH and therefore that practical FINCH microscopy is capable of matching the idealized theoretical capabilities provided that the optics in the microscope can produce an unaberrated defocus beam from which the FINCH system can create two similar structureless Beams for FINCH interference.

[0073] Figure 19 continues this summary by showing that it is possible for different objectives to produce markedly different beams that then are processed by the FINCH optics to produce either excellent holographic data or significantly aberrated holographic data. The top two rows are identical to Figure 18 for reference. Row 3 shows fluorescence holographic data of a 200 nm PSF bead imaged through an objective (Zeiss 40x fluar oil objective, 1.3 NA) with the ability to produce an unaberrated defocus beam that is used to form high quality raw and complex holograms and a reconstructed image without halo. Note that another objective (Zeiss 63x plan-apo oil objective, 1.4 NA) was able to perform similarly. Conversely, Row 4 shows data from a similar bead taken with an objective (Nikon 60x TIRF oil objective, 1.49 NA) that is not able to produce an unaberrated beam; the resultant Beams are quite dissimilar and structured, and the raw and complex holograms obviously aberrated, producing a reconstructed image with significant halo. As with the laser / objective data in Row 4 of Figure 18, the aberrated fluorescence data can be cleaned up by spatial filtering as shown in Row 5 to produce high-quality Beams and FINCH holographic data including a reconstructed image with no halo.

[0074] Finally, the teachings discussed above also explain the observations represented in the images of Figures 20 and 21. Figure 20 shows widefield and FINCH data of a microtubule sample (GattaQuant 4C slide) taken with the Nikon TIRF objective discussed above. The widefield data is a typical fluorescence image, while the FINCH reconstructed image is aberrated and unclear. Note the inset image in the upper left corner of the FINCH image, showing the (aberrated) FINCH PSF of the FINCH system that was used to take the microtubule image. Figure 21 shows widefield and FINCH images of a different microtubule cell from the same slide as used in Figure 20, imaged with the 63x Zeiss objective discussed above. The FINCH PSF in the upper left corner of the FINCH image is much better than that in Figure 20. Note that the widefield image is typical of widefield images of this type of sample, while the FINCH image is of improved contrast and resolution, demonstrating fulfillment of the promise of the idealized FINCH concept. In full summary, the use of a well-selected or designed objective dramatically increases the performance of FINCH microscopy and enables realization of the theoretical potential. A limited number of Zemax files are available for microscope objectives from different manufacturers, (Zhang and Gross, "Systematic design of microscope objectives. Part I: System review and analysis" {https: / / doi.org / 10.1515 / aot-2019- 0002) 2019 and Kurvits, Jiang and Zia, "Comparative analysis of imaging configurations and objectives for Fourier microscopy" {https: / / opg. optica. org / josaa / abstract.cfm?uri=josaa-32-ll-2082#top) 2015) to analyze objective performance and thereby determine optimal objectives to use for FINCH microscopy. Zemax modeling can serve as a good tool to examine the shapes and aberrations of the defocus beams necessary for FINCH and predict which objectives will work well with FINCH.

[0075] STRATEGIES FOR ELIMINATING ABERRATIONS There are different corrective approaches that may be taken in order to produce a FINCH system in which two symmetrical and identical beams interfere with each other. Consider Figures 22-24 which depict that optical aberrations induced by any part of the optical system can result in imperfectly matched or overlapped beams that reduce the FINCH hologram quality. Figure 22 depicts the two FINCH beams, tracing them from the light received from the object through the creation of the fdl and fd2 beams that create independent images. With aberration-free optics, the wave vectors of the original beam and then of the two beams propagate along the same axis, which is the optical axis of the system. Thus the beams are perfectly overlapped at the hologram recording plane and the interference efficiency and quality is maximized. As shown in Figure 23, an aberration may be introduced at the first lens in the system, the objective lens. In many microscopy systems, the objective lens is the most high-tolerance part that is most likely to introduce large aberrations. In the first case exemplified here as a tip / tilt aberration from the objective causes the wave vector of the light beam from the sample to propagate at a slight angle to the system optical axis, and as a result the two beams that are produced by the birefringent lens are no longer collinear - the new wave vector of each beam leaves the BRL at a different angle (ai and a2) to the system optical axis, causing imperfect overlap of the two beams at the hologram recording plane. While the beams do still overlap partially, there is at every distance along the beam paths a part of one of the beams that does not overlap any part of the other beam, and this missing overlap leads to reduced interference efficiency and image quality. In Figure 24, the primary lens is not aberrated but a tip / tilt aberration in the BRL causes the two beams to propagate away from the BRL with different wave vectors, again causing imperfect beam overlap. Note that in Figures 23 and 24 the aberration considered is tip / tilt that damages the colinear propagation of the two beams used to create the hologram. However, the concept applies also to aberrations that do not affect collinearity but instead only damage the phase profile of at least one of the beams, such as coma, spherical aberration or astigmatism amongst others. Aberrations that do not affect overlap or collinearity may still degrade the FINCH hologram even though that is not depicted in Fig. 22-24.

[0076] In one corrective approach, an entire FINCH system may be designed all together, so that all components work together and any one component may perform some or all of the optical correction for one or more other components. Such an approach could be the simplest way to design single-purpose optical systems that have maximum optimization for their specific purpose. For example, a metrology system designed only to image circuit boards at a wavelength of 350 nm could neglect chromatic aberrations in its design and instead be designed only for correction of the planatic and monochromatic aberrations such as spherical aberration, coma, astigmatism, and field curvature. In another example, a biomedical screening instrument designed only to measure colocalization of two specific proteins with specific conjugated dyes could be designed with chromatic correction only for those two dye's specific wavelengths without requiring chromatic correction for any other wavelength. Both of these examples reduce the manufacturing complexity required since they do not attempt to create a design that can readily be applied to any task. A disadvantage is that individual systems must be designed for each purpose, even though each system that is made can have reduced complexity due to purpose-specific design.

[0077] One such purpose-built system could be based on a telecentric imaging system. Telecentric imaging is a type of imaging, well-known to one skilled in the art, in which light from all points in an object is used to create an image in which there is no change in lateral magnification throughout all the 3D spaces containing the object and image. This is always done by placing an aperture called the telecentric stop at the focal plane of at least one lens, which forces all the light beams from any part of the object to propagate along a direction parallel to the system optical axis, in at least the object space (between the object and the first lens in the system) or the image space (between the last lens of the system and the image). Telecentric imaging is used advantageously in applications including amongst many others metrology and machine vision due to its low distortion, and constant magnification. However, telecentric images do still have a limited depth of field / focus and do also lose three dimensional information about the object being imaged. A purpose-built telecentric FINCH imaging system provides new advantageous features such as greater depth of field / focus, three-dimensional information, and higher lateral resolution to telecentric imaging.

[0078] To consider telecentric optics in general, consider a double-telecentric design as shown in Figure 25, that is telecentric in both object and image space. As is well known to one skilled in the art, in a telecentric system there is a physical stop (telecentric stop) at the focal plane of at least one of the lenses that causes the pupil of said lens to go to infinity. Figure 25 shows two lenses arranged in double telecentric condition, wherein the lens pair is separated by the sum of their focal lengths, and a stop is placed at their mutual focal plane, centered on the optical axis. The result of this is that the chief rays of axial object points, shown by the solid gray lines in Figure 25, all are parallel to the optical axis between the object plane and Lens 1, and between Lens 2 and the image plane. As shown by Figure 25 part (b), when an object is moved away from its initial Z-position in such an arrangement, but kept at the same XY (radial) position, the chief ray stays parallel to the optical axis at the same radial position. Therefore, the out-of-focus beams also project along an axis that is parallel to the optical axis in both object space and image space. Such a system has constant image magnification for any location in object space.

[0079] One very important aspect of the optical design of FINCH systems is the requirement that the pair of beams generated by the specialized lens from each point in the object must be totally concentric with each other in order to achieve the best quality un-aberrated holograms and images. In fact, for sufficiently low degrees of concentricity, there will be no interference to record and therefore no hologram at all. Perfect concentricity may be universally obtained for the axial object point in any ideally aligned image system; however for object points (that shall be referred to herein as radial points) that are displaced in the XY (transverse) plane orthogonal to the optical propagation "Z" axis, concentricity in most systems will degrade in direct proportion to the radial distance from the Z axis. This characteristic will be referred to herein as the "radial problem", or "FINCH vignetting". This is due to the fact that by the classical laws of optics, the chief rays of the beams originating from any given radial object point and impinging on a lens will leave the lens at an angle dependent on the focal length of the lens. Since the specialized FINCH birefringent lens essentially has two focal lengths, each of the beams in a given pair will have a different chief ray angle as it leaves the FINCH lens, which dictates that the two beams propagate along different wave vectors. As the rays propagate further away from the lens to the hologram plane, the two beams in each pair lose concentricity as a result of their different propagation directions, leading to reduced beam overlap and interference efficiency.

[0080] The issue of reduced beam overlap with radial displacement from the system optical axis constitutes an aberration in the FINCH system. This may be solved by integrating a BRL into a telecentric optical system and designing the full system to eliminate the FINCH vignetting as well as any other aberrations. The FINCH vignetting is solved as follows, while the remainder of the aberrations to be eliminated may be corrected by other standard lens design methods. As shown in Figure 26, a birefringent lens (BRL) 2608 can be placed at the location of the telecentric stop 2602, so that all beams received from the object 2604 through lens 1 2606 are exactly centered on the BRL. The BRL affects each beam differently, producing the pair of differentially focused beams 2610 and 2612 that is required for FINCH. Crucially, since the beams were centered on the BRL as they passed it, their chief rays were not bent and their propagation direction was therefore unaltered, so each pair of beams remains perfectly concentric. Lens 2 2607 then focuses each beam pair with both their chief rays parallel to the optical axis, ensuring perfect overlap for all radial points at the hologram recording plane 2614. An optical setup was constructed as described in Figure 26, with Lens 1 having focal length 125 mm, Lens 2 having focal length 200 mm, and the object being located approximately 135 mm away from Lens 1. The magnification inherent in this optical system (200 / 125 = 1.6X) results in an increase in the distance between the two image planes produced by the optical system. The object was a reflective USAF test pattern mask, and it was illuminated in an epi-illumination technique with light of ~20 nm bandwidth. The birefringent lens was a PCX lens with curvature -457 mm made from alpha-BBO. A polarizing beam splitter was installed between the object and Lens 1, and a BBO compensating plate and broadband quarter wave plate were installed between Lens 2 and the polarized camera, which was at the hologram plane of maximum overlap. Standard images were recorded at both the short and long (fdl and fd2 respectively) image planes, and a hologram was recorded at the hologram plane 2614 and was reconstructed to a focused image. The resulting images are shown in the insets in the lower right corner; the images marked fdl image, fd2 image and FINCH image are all exactly the same size, and the FINCH image is of high quality, showing that telecentricity was maintained and the interference efficiency was high.

[0081] As incorporated with a telecentric system above, BRL-enabled FINCH brings the advantages of its well-characterized three-dimensional (3D) imaging to telecentric imaging. By definition, previous telecentric imaging is not capable of distinguishing 3D information in an object or providing any 3D perspective. Telecentric FINCH, however, can reconstruct different object planes in an object that is outside the depth of focus of the telecentric system, and can identify what the axial (depth) location of different parts of the object are, an ability not currently available in telecentric imaging.

[0082] In another corrective approach, a FINCH system can be considered as a sum of two independent systems, a FINCH-specific system and a general system, that are connected to each other for a combined purpose. In this case, the goal of the approach is to have a FINCH-specific system containing only the optical components - Polarizer, BRL and associated optics, Quarter-waveplate, polarization camera - necessary to generate two (ideally perfect) beams from a single (ideally perfect) received beam, that is ready to be combined with any other system that can provide a perfect beam for the FINCH optics to receive. The FINCH-specific optical system must be optimized and corrected independently, and the general system also must be optimized and corrected independently. This approach has the advantage that a single FINCH-specific system can be constructed that can interface to any general optical system, lowering the cost and time-to-market. This approach still requires the optimization of the entire general system beyond the optimization systems usually undergo for standard purposes. In another corrective approach, the FINCH-specific system is optimized independently for FINCH holography on a perfect received beam. The general system is optimized for its own purpose without requiring a perfect non-aberrated output beam to transmit to the FINCH-specific system. Then a third system, the corrective system, is provided to act as the interface between the general and FINCH-specific systems. This approach may in fact be the most optimal corrective approach since any off-the-shelf general system can be interfaced with a single FINCH-specific system, saving time and cost on developing new general systems or multiple single-purpose systems, while only designing one (or few) FINCH-specific systems. The corrective system can be dedicated solely to correcting whatever known aberration exist in the general system and making any further adjustments necessary to allow the FINCH-specific system to perform to its maximum capabilities. There are many elements that can be used for correction, including SLMs, deformable mirrors, adjustable lens assemblies and others. An example of a corrective system used to correct a known aberration is found in "Any immersion remote refocus (AIRR) microscopy" (published online by Millett-Sikking, Alfred, 2022, found at https: / / amsikking.github.io / any_immersion_remote_refocus_microscopy) in which a zoom-lens system is used in place of a tube lens in an after-market add-on that converts a standard microscope into a remote-refocusing microscope. The known aberration in that case is sample-medium induced spherical aberration, for which the zoom-lens performs a correction that is adjustable based on a rational understanding of the refractive index mismatch of the actual sample medium and the objective design.

[0083] With respect to the above teachings regarding correction approaches, the inventors have determined that the current FINCH microscope may produce pairs of interfering Beams 1 and 2 (fdl and fd2) with asymmetry and discrepancies between them. The inventors have further found that the asymmetry and discrepancies are due to the microscope objectives used in the microscope. Note that while the following teachings are made with reference to microscope objectives as the primary cause of aberrations, these teachings are not limited to objectives and are analogously applicable to aberrations, asymmetry and discrepancies caused by any other element. With the conclusion that the objective is the main source of aberrations in practice for FINCH microscopy, it is necessary to propose methods for eliminating or correcting the aberrations due to the objective. Generally, aberration removal or correction may take one of four broad approaches:

[0084] 1. Prevent aberrations: Create beams of light from the object that have as few aberrations as possible in the defocus parts of the beam. 2. Remove aberrations: Create aberrated beams of light from the object, and then spatially filter out the aberrations with a spinning disk or other filtering approach.

[0085] 3. Correct aberrations: Create aberrated beams of light from the object, and use other optical elements such as deformable mirrors, spatial light modulators, aspheric lenses or others to correct the aberrations.

[0086] 4. Compensate for aberrations: in the computation of the final reconstructed image, use a numerical adjustment to the image creation (Fresnel propagation or other) process to compensate for the aberrations in the recorded hologram and prevent their propagation through to the final image.

[0087] 1. Preventing aberrations

[0088] In the matter of preventing aberrations, consider that modern microscope objectives are designed to obtain the best image possible at a single plane of focus and to overcome various external factors that can reduce the resultant quality of an image. These variables include wavelength, temperature, immersion media, coverslip thickness and a variety of other less major factors including the Seidel and Zernike aberrations. Objectives and imaging systems are designed to obtain the best image at a single plane of focus and are not designed to provide defocus beams that possess the fewest possible aberrations and least structure. In distinction to this FINCH requires defocus beams, i.e. the beams above and below the plane of focus, that have the least possible structure and fewest aberrations, and can tolerate an objective plane of focus that is not as well corrected as others. In many applications, a FINCH system might further need only to work at a single wavelength, which can reduce the complexity of the objective used and reduce the need for large corrections to be performed in the objective, which we have shown may lead to structure in the defocus beam.

[0089] Widefield, confocal, phase contrast, TIRF, DIC, polarization, reflection, etc. and color correction lenses are all optimized during the design phase for the imaging method they serve. In each case they are designed to provide the highest resolution possible at the plane of focus. These lenses are not optimal for holographic imaging in which each image beam originating from an object at focus ideally produces two defocus beams with equal intensity profiles and roughly opposite phases, ultimately interfering with each other to create a hologram that accurately represents the 3D volume of the object.

[0090] The inventors have discovered this fact and have invented a variety of methods and apparatus to allow for the efficient imaging of objects with better than optical resolution in a variety of ways. One such way is the design of new optics to create, from each light beam from the object, two out of focus beams with equal intensities and roughly opposite phase characteristics. In the case of microscope objectives these lenses can be called H-objectives, designed for various specialized tasks and to provide ideal defocus beams for each specialized task (H-Widefield, H-confocal, H-color corrected, H-TIRF, etc.). All of these objectives will give enhanced resolution when the microscope is operated in holographic mode.

[0091] Modern lens design software such as ZEMAX can be used to design objective lenses with the appropriate characteristics needed for FINCH imaging, i.e. good in and out of focus uniform beams that also provide good resolution at the plane of focus.

[0092] 2. Removing aberrations

[0093] An approach that was demonstrated in Figures 13-14 and related discussion shows that the process of spatially filtering the light prior to its passage through the FINCH optics improves the beams shapes, symmetry and image quality. This method, has been established to work on multiple independent microscope implementations. For even higher efficiency where confocality is not required, a Nipkow disk with much higher density of pinholes could be fabricated for use; since the purpose of the pinholes is not to establish confocality but only to spatially filter light beams, the density of the pinholes could be increased at least 5-10-fold with a concurrent proportional improvement in image intensity over standard Nipkow disks used in confocal microscopy. Another potential method is to use other spatial filtering means such as an array of single mode optical fibers, solid state spatial filters or a photonic crystal optical element that only permits gaussian modes to propagate through it.

[0094] 3. Correcting aberrations

[0095] There are also methods for correcting aberrations in the light beams as opposed to preventing them or removing them. One common method for correcting spherical aberration, for example, is to use an aspheric lens element at a pupil plane (such as the plane wherein the BRL is located in the FINCH microscope). Another method would be to use a deformable mirror or a spatial light modulator (SLM) to apply beam corrections by analyzing a given objective lenses and applying Zernike or Seidel corrections.

[0096] To provide more detail about using aspheric lenses to correct aberrations, consider Figures 27 and 28, which demonstrate applying Zemax analysis and design for FINCH with a TIRF or regular objective with a corrective strategy of simply adding an aspheric lens to the optical train. Figure 27 contains through- focus spot diagrams of a 60x 1.49 NA TIRF objective and a 60x 1.4 NA standard objective as well as corresponding Seidel diagrams showing the Seidel coefficients of the spherical aberration (SA) of all the lens components in a graphical format. The spot diagrams are an indication of the geometric shape of the beam of light as it goes in and out of focus, which is very important for the creation of high quality FINCH holograms. The data show that the 60xTIRF has significant asymmetry between the beam going into focus (-20, -10 mm) and coming out of focus (10, 20 mm) due to strong SA, as confirmed by the total SA Seidel coefficient of -3.32 mm indicated on the Seidel chart below. This is consistent with the data for the 60x TIRF objective shown in Figures 6, 14, 19, and 20 which demonstrate suboptimal performance of FINCH when used with a 60x TIRF objective and no correction by confocal or spatially filtered imaging. On the other hand, the diagrams in Figure 27 for the 60x standard objective show much less asymmetry and SA with a total SA Seidel coefficient of 0.24. This order-of-magnitude improvement in a significant aberration shows clearly how much difference can be made by the choice of optimal objectives. Figure 28 shows the effect of one corrective strategy, adding an aspheric lens to fix the SA. The optical diagrams show that the addition of a single corrective element, an aspheric lens, is enough to dramatically reduce the SA by multiple orders of magnitude from -3.332 to -0.0009 and from 0.24 to -0.0008. The aspheric lenses in Figure 28 were designed in Zemax and have a conic constant of zero, with both sides of the lens having infinite major curvature (each side is piano) but with one surface having a fourth-order coefficient with an absolute value on the order of between 6 to 9 x 10'6. Note that these aspheric corrective lenses were designed to provide SA correction without adding any extra focusing power to the system. Further, they were designed with a 10 mm center thickness. These parameters could easily be changed to accommodate other systems or placement at different locations in the optical train. For example, in Zemax simulation data (not shown) of a FINCH microscope of the type of 400, other aspheric correctors with less thickness and larger fourth order coefficients were placed at the relayed objective pupil plane just prior to the BRL 203 in Figure 4, and successfully reduced the overall SA of the microscope to effectively zero.

[0097] 4. Computational correction

[0098] The last class of solutions to the problem of aberrations in FINCH holograms induced by asymmetrical beams in the hologram formation process is to apply a correction factor ^?to either the raw hologram or the reconstruction function in equation 2, as exemplified in equation 5. The correction could be accomplished by multiplying either the complex hologram (as in equation 5) or the reconstruction function such as the IRF or the OTF of Equations 2 and 3 (which is complex-valued) with a corrective phase matrix such as a Zernike phase polynomial. (equation 5) The Zernike coefficients can be iteratively adjusted to improve the correction that is applied. The optimal set of coefficients can be determined for any particular objective by using PSF methods; ie an aberrated PSF hologram can be recorded with the objective, and the Zernike correction can be iteratively adjusted until a satisfactory image spot with no halo (sidelobes) is produced. The set of Zernike coefficients that is thus generated can then be used to generate a correction factor for the reconstruction of images from other sample objects.

[0099] According to an embodiment an electromagnetic imaging apparatus is provided. The apparatus is configured to create two distinct electromagnetic waves from each electromagnetic wave received from any point of an object, wherein said two distinct electromagnetic waves perfectly interfere at any plane as if each of the two distinct electromagnetic waves originated from a perfectly collimated laser with no aberrations. The electromagnetic radiation may be coherent or incoherent. The optical system may be telecentric and the creation of the two colinear waves from the received wave may be accomplished at the location of the telecentric stop.

[0100] According to another embodiment an electromagnetic imaging method is provided. The method comprises: creating two distinct electromagnetic waves with no aberrations from each electromagnetic wave received from an object, wherein said two distinct electromagnetic waves have wave characteristics of a perfectly collimated laser beam; and causing the two distinct electromagnetic waves to interfere at any plane.

[0101] According to another embodiment an electromagnetic imaging apparatus is provided. The apparatus comprises: a means to create two distinct defocused beams of light from each original beam received from an object, wherein said two distinct defocused beams perfectly interfere at any plane after the apparatus, as if each of the distinct defocused beams originated from a perfectly collimated and nonaberrated laser. The means to create interfering beams may comprise a lens system, electromagnetic beam system, SLM, deformable mirror system, multiple beam-splitter system, multifocal lens system, or any other beam separating system. All of the optics and other elements in the apparatus including the means to create two beams from a single received beam may be constructed by design to balance and correct each other in order to produce the distinct beams of perfect character. Alternatively, all optics and other elements of the apparatus prior to the means that create the two beams from the beam received from the object may be designed together for the purpose of supplying a perfect unaberrated beam to the means that creates the two beams. According to another embodiment an electromagnetic imaging method is provided. The method includes creating two distinct defocused beams of light from each original beam received from an object, wherein said distinct defocused beams perfectly interfere at any plane after the apparatus, as if each of the distinct beams originated from a perfectly collimated non-aberrated laser.

[0102] According to another embodiment an optical system is configured to receive, at a first subassembly, EM (electromagnetic) waves from an object wherein the first subassembly is configured to convert said EM waves into altered EM waves that propagate away from the first subassembly with one or more optical aberrations not present in the altered EM waves, and produce, after transmission through one or more further optical assemblies, an unaberrated interference pattern that is recorded with a recording means. The first assembly may include a simple or compound lens with a composition of surfaces shapes and materials configured to produce altered waves that lack at least one of the well- known optical aberrations, for at least one wavelength of EM radiation. Each of the altered waves, at the plane of the recording means, has been transformed into two descendant waves in different states of defocus, each of which lacks one or more of the optical aberrations known to one skilled in the art and listed elsewhere herein.

[0103] According to another embodiment an optical system is provided. The optical system may be configured to receive, at a first subassembly, EM waves from an object wherein the first subassembly is configured to create altered waves that propagate away from the first subassembly with one or more optical aberrations present in the altered waves, and to remove said aberrations with a spatial filtering means, and produce, after transmission through one or more further optical assemblies, an unaberrated interference pattern that is recorded with a recording means. The spatial filtering means may be a scanned array of pinholes of approximately the size of the airy disk of the EM radiation as focused onto the location of the spatial filter means. The spatial filter means may alternatively be a scanned array of slits or other apertures with at least one dimension of about the size of the airy disk of the EM radiation as focused onto the location of the spatial filter means. After the spatial filtering has been applied, each of the filtered altered waves, at the plane of the recording means, has been transformed into two descendant waves in different states of defocus, each of which lacks one or more of the well-known optical aberrations.

[0104] According to another embodiment an optical system is provided. The optical system is configured to receive, at a first subassembly, EM waves from an object wherein the first subassembly is configured to create altered waves that propagate away from the first subassembly with one or more optical aberrations present in the altered waves, and to correct said aberrations with a corrective optical means, and produce, after transmission through one or more further optical assemblies, an unaberrated interference pattern that is recorded with a recording means. The corrective optical means may include a static optical element with materials and surface features configured to invert or otherwise correct one or more of the common aberrations that is present in the altered waves. Alternatively, the corrective optical means may include an optical element with materials and surface features configured to invert or otherwise correct one or more of the common aberrations that is present in the altered waves, and wherein said optical element is movable to different positions and performs differing optical corrections according to the specific location in which it is located, to correct for different optical aberrations in the altered waves. Alternatively, the corrective optical means may include more than one optical element, separate from each other and able to move independently from each other, each with materials and surface features configured to invert or otherwise correct one or more of the common aberrations that is present in the altered waves, and wherein the total correction applied by the means is changed based on the relative positions of the optical elements relative to each other and the first subassembly of the optical system. Each of the corrected altered waves, once it has propagated to the plane of the recording means, has been transformed into two descendant waves in different states of defocus, each of which lacks one or more of the optical aberrations it originally contained.

[0105] The correction performed in this embodiment may be applied by means of a deformable mirror, by means of a spatial light modulator, by a means including at least one aspheric lens, or by using Zernike coefficients derived from PSF images recorded without correction to the corrective optical means.

[0106] According to another embodiment an optical system is provided. The embodiment includes an optical system configured to receive, at a first subassembly, EM waves from an object wherein the first subassembly is configured to create altered waves that propagate away from the first subassembly with one or more optical aberrations present in the altered waves, and produce, after transmission through one or more further optical assemblies, an aberrated interference pattern that is recorded on a recording means, and to correct the aberrations in the recorded interference pattern with a computational means. The computational means may include creating a complex-valued representation of the recorded interference pattern, and applying a pre-calculated correction function to remove the aberrations in the recorded interference pattern. Alternatively, the computational means may include performing an iterative correction to the recorded interference pattern until a given quality metric for the corrected interference patter is reached. The computational means may include an iterative process comprising: producing an image of the object from the interference pattern; analyzing the image for aberrations and defects, and deducing from the analysis a correction to apply to the interference pattern and using the corrected interference in a repeat of the first step of the algorithm unless the analysis indicates an acceptably low level of aberrations and defects in the image is obtained, in which case the iterative process is stopped and the corrected interference pattern is accepted as the best-corrected interference pattern.

[0107] Numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.

Claims

CLAIMS1. An electromagnetic imaging apparatus comprising a first optical assembly and one or more second optical assemblies and configured to: receive, at the first optical assembly, electromagnetic (EM) waves from an object, wherein the received EM waves include at least one optical aberration; convert, at the first optical assembly, the received EM waves into altered waves that propagate away from the first optical assembly lacking the at least one of the optical aberrations of the received waves, and generate, after transmission of the altered waves through the one or more second optical assemblies, an unaberrated interference pattern on a surface.

2. The apparatus of claim 1, further comprising a recording device configured to record the unaberrated interference pattern.

3. The apparatus of claim 1, wherein the first optical assembly includes a simple or compound lens with a composition of surfaces shapes and materials configured to produce the altered waves for at least one wavelength of EM radiation.

4. The apparatus of claim 1, wherein the one or more second optical arrangements includes at least one second lens configured to transform, each of the altered waves, into two descendant waves in different states of defocus at the surface, each of two descendent waves is free of at least one optical aberration present in the EM wave received from the object.

5. The apparatus of claim 1, wherein the first optical assembly includes a spatial filter configured to remove optical aberrations from the EM waves received from the object.

6. The apparatus of claim 5, wherein the spatial filter is a pinhole, with a diameter on the order of the diameter of the Airy disk of the EM radiation, located at a focal plane of the EM waves received from the object, wherein the pinhole's position in the focal plane is scanned to filter all parts of the focal plane.

7. The apparatus of claim 5, wherein the spatial filter is an array of pinholes, with a common diameter on the order of the diameter of the Airy disk of the EM radiation, located at a focal plane of the EM waves received from the object, wherein the array of pinholes is systematically scanned over an entire area of the focal plane to filter all parts of the focal plane.

8. The apparatus of claim 5, wherein the spatial filter is an array of slits with at least one dimension on the order of the diameter of the Airy disk of the EM radiation, wherein the array of slits is scanned over an entire area of the focal plane to filter all parts of the focal plane.

9. The apparatus of claim 2, wherein the first optical assembly includes a static optical element with materials and surface features configured to correct at least one aberration that is present in the received EM waves.

10. The apparatus of claim 1, wherein the first optical assembly includes an aspheric lens.

11. The apparatus of claim 1, wherein the first optical assembly includes a deformable mirror.

12. The apparatus of claim 1, wherein the first optical assembly includes a spatial light modulator.

13. A telecentric electromagnetic imaging apparatus, said apparatus designed to create two distinct electromagnetic waves from each electromagnetic wave received from any point of an object, wherein said distinct waves are caused to interfere with each other to produce a hologram of said object.

14. The apparatus of claim 13, wherein the means to create said two distinct waves is located at a telecentric stop of the apparatus.

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