Light projection using superposition gaussian beams

Abstract

Optical systems, instruments and methods for pro j ecting light beams with enhanced shape and focal properties are disclosed. An apparatus for optical proj ection includes a light source, which is configured to output a coherent beam of optical radiation, and an optical phase modulator. The optical phase modulator is configured to modulate the beam with a spatial modulation profile including a superposition of respective transfer functions of multiple lenses with different foci so as to generate a superposition Gaussian beam ( SGB).

Description

[0001] LIGHT PROJECTION USING SUPERPOSITION GAUSSIAN BEAMS

[0002] CROSS-REFERENCE TO RELATED APPLICATION

[0003] This application claims the benefit of U.S. Provisional Patent Application 63 / 649,388, filed May 19, 2024, which is incorporated herein by reference.

[0004] FIELD

[0005] The present invention relates generally to optical systems, instruments and methods, and particularly for projecting light beams with enhanced shape and focal properties .

[0006] BACKGROUND

[0007] Light-sheet microscopy (LSM) is a microscopy technique in which a thin sheet of light illuminates a sample perpendicular to the direction of observation. It is commonly used in various fields of biology. The resolution is impaired compared to confocal microscopy, but the benefits are superior optical sectioning along the axial direction and very high speed of acquisition. The light sheet itself is typically generated using a Gaussian beam focused with a cylindrical lens. Alternatively, a Bessel beam, which has better non-diffracting properties, may be scanned rapidly in a transverse direction. A disadvantage of the Bessel beam light sheet is its sidelobes, which reduce the sectioning resolution.

[0008] In microscopy in general there is always a need to improve imaging capabilities. Improvement of tens of percent in resolution or acquisition time is considered to be significant. For LSM, the shape of the light beam that is used is crucial in determining the imaging properties. The beam is required to be as flat as possible, as long as possible, uniform in its intensity, and preferably without side lobes of any kind.

[0009] SUMMARY

[0010] Embodiments of the present invention provide systems and methods for designing non-diffracting Gaussian-like beams .

[0011] In accordance with aspects of the present disclosure, an apparatus for optical projection includes a light source, which is configured to output a coherent beam of optical radiation, and an optical phase modulator. The optical phase modulator is configured to modulate the beam with a spatial modulation profile including a superposition of respective transfer functions of multiple lenses with different foci so as to generate a superposition Gaussian beam (SGB) .

[0012] In various embodiments of the apparatus, the transfer functions correspond to spherical lenses, whereby the optical phase modulator generates a stigmatic SGB.

[0013] In various embodiments of the apparatus, each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single spot, whose distance from the optical phase modulator is characterized by a given focal length.

[0014] In various embodiments of the apparatus, the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is more than or equal to 0.06 and less than or equal to 0.22.

[0015] In various embodiments of the apparatus, the resolution of spacing between the foci of the multiple lenses is smaller than or equal to half of the Rayleigh range of the beam with the shortest focal distance realized by a transfer function of the superposition of transfer functions .

[0016] In various embodiments of the apparatus, the transfer functions correspond to cylindrical lenses, whereby the optical phase modulator generates an astigmatic SGB.

[0017] In various embodiments of the apparatus, the astigmatic SGB includes a light sheet, to be directed to impinge on a sample in a light-sheet microscope.

[0018] In various embodiments of the apparatus, each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single line, whose distance from the optical phase modulator is characterized by a given focal length.

[0019] In various embodiments of the apparatus, the modulation is performed such that the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is less than or equal to 0.09 and more than or equal to 0.04.

[0020] In various embodiments of the apparatus, the resolution of spacing between the foci of the multiple lenses is smaller than or equal to a quarter of the Rayleigh range of the beam with the shortest focal distance realized by a transfer function of the superposition of transfer functions . In various embodiments of the apparatus, the SGB propagates along a straight line.

[0021] In various embodiments of the apparatus, the different foci are equidistant along a line.

[0022] In various embodiments of the apparatus, the SGB follows a curved trajectory.

[0023] In various embodiments of the apparatus, the optical phase modulator includes a spatial light modulator (SLM) .

[0024] In various embodiments of the apparatus, the optical phase modulator includes one or more diffractive or refractive optical elements.

[0025] In accordance with aspects of the present disclosure, a method for optical projection includes modulating a projected coherent beam of optical radiation with a spatial modulation profile including a superposition of respective transfer functions of multiple lenses with different foci so as to generate an SGB.

[0026] In various embodiments of the method, the method further includes projecting the beam.

[0027] In various embodiments of the method, the method further includes calculating the superposition of respective transfer functions.

[0028] In various embodiments of the method, the transfer functions correspond to spherical lenses, and generating the SGB includes generating a stigmatic SGB.

[0029] In various embodiments of the method, each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single spot, whose distance from the optical phase modulator is characterized by a given focal length. In various embodiments of the method, the modulation is performed such that the ratio between the Rayleigh range of a beam reali zed by a trans fer function of the superposition of trans fer functions having the middle focal length and the length of the SGB is less than or equal to 0 . 22 and more than or equal to 0 . 06 .

[0030] In various embodiments of the method, the resolution of spacing between the foci of the multiple lenses is smaller than or equal to hal f of the Rayleigh range of the beam with the shortest focal distance reali zed by a trans fer function of the superposition of trans fer functions .

[0031] In various embodiments of the method, the trans fer functions correspond to cylindrical lenses , wherein generating the SGB includes generating an astigmatic SGB .

[0032] In various embodiments of the method, the astigmatic SGB includes a light sheet , and the method further includes directing the SGB to impinge on a sample in a light-sheet microscope .

[0033] In various embodiments of the method, each trans fer function of the superposition of trans fer functions reali zes the focusing of a beam to a given single line , whose distance from the optical phase modulator is characteri zed by a given focal length .

[0034] In various embodiments of the method, the modulation is performed such that the ratio between the Rayleigh range of a beam reali zed by a trans fer function of the superposition of trans fer functions having the middle focal length and the length of the SGB is less than or equal to 0 . 09 and more than or equal to 0 . 04 . In various embodiments of the method, the resolution of spacing between the foci of the multiple lenses is smaller than or equal to a quarter of the Rayleigh range of the beam with the shortest focal distance reali zed by a trans fer function of the superposition of trans fer functions .

[0035] In various embodiments of the method, the modulating of the beam is performed via an SLM .

[0036] In various embodiments of the method, the modulating of the beam is performed via one or more di f fractive or refractive optical elements .

[0037] In various embodiments of the method, modulation is performed such that the SGB propagates along a straight line .

[0038] In various embodiments of the method, the di f ferent foci are equidistant along a line .

[0039] In various embodiments of the method, each lens of the multiple lenses is shi fted or tilted to a di f ferent transverse location such that the SGB follows a curved tra j ectory .

[0040] In accordance with aspects of the present disclosure , a computer program product includes a computer-readable storage medium having computer-executable instructions for modulating a proj ected coherent beam of optical radiation with a spatial modulation profile including a superposition of respective trans fer functions of multiple lenses with di f ferent foci so as to generate an SGB .

[0041] In various embodiments of the computer program product , the computer-readable storage medium has further computer-executable instructions for calculating the superposition of respective trans fer functions . In various embodiments of the computer program product, the transfer functions correspond to spherical lenses, so as to generate a stigmatic SGB.

[0042] In various embodiments of the computer program product, each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single spot, whose distance from the optical phase modulator is characterized by a given focal length.

[0043] In various embodiments of the computer program product, the modulation is performed such that the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is less than or equal to 0.22 and more than or equal to 0.06.

[0044] In various embodiments of the computer program product, the resolution of spacing between the foci of the multiple lenses is smaller than or equal to half of the Rayleigh range of the beam with the shortest focal distance realized by a transfer function of the superposition of transfer functions.

[0045] In various embodiments of the computer program product, the transfer functions correspond to cylindrical lenses, so as to generate an astigmatic SGB.

[0046] In various embodiments of the computer program product, the astigmatic SGB includes a light sheet, to be directed to impinge on a sample in a light-sheet microscope .

[0047] In various embodiments of the computer program product, each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single line, whose distance from the optical phase modulator is characterized by a given focal length.

[0048] In various embodiments of the computer program product, the modulation is performed such that the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is less than or equal to 0.09 and more than or equal to 0.04.

[0049] In various embodiments of the computer program product, the resolution of spacing between the foci of the multiple lenses is smaller than or equal to a quarter of the Rayleigh range of the beam with the shortest focal distance realized by a transfer function of the superposition of transfer functions.

[0050] In various embodiments of the computer program product, modulation is performed such that the SGB propagates along a straight line.

[0051] In various embodiments of the computer program product, the different foci are equidistant along a line.

[0052] In various embodiments of the computer program product, each lens of the multiple lenses is shifted or tilted to a different transverse location such that the SGB follows a curved trajectory.

[0053] BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The above and other aspects and features of the disclosure will become more apparent in view of the following detailed description when taken in conjunction with the accompanying drawings wherein like reference numerals identify similar or identical elements. FIG . 1 is an illustration of an exemplary optical scheme for generating SGB illumination in a light-sheet microscope , in accordance with aspects of the disclosure ;

[0055] FIG . 2 is a flow diagram of a method for optical proj ecting, in accordance with aspects of the disclosure ;

[0056] FIG . 3 includes graphs presenting an astigmatic SGB in comparison to an astigmatic Gaussian beam, in accordance with aspects of the present disclosure ;

[0057] FIG . 4 includes graphs presenting the Modulation Trans fer Functions (MTFs ) of the astigmatic SGB in comparison to the astigmatic Gaussian beam of FIG . 3 at di f ferent planes along propagation, in accordance with aspects of the disclosure ; and

[0058] FIG . 5 includes graphs presenting a stigmatic SGB in comparison to a stigmatic Gaussian beam, in accordance with aspects of the disclosure .

[0059] It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale . For example , the dimensions and / or aspect ratio of some of the elements can be exaggerated relative to other elements for clarity . Further, where considered appropriate , reference numerals can be repeated among the figures to indicate corresponding or analogous elements throughout the serial views .

[0060] DETAILED DESCRIPTION

[0061] Light-sheet microscopy is characteri zed by employing light intensity distribution in the form of a thin sheet , which selectively illuminates the focal plane of a microscope ' s detection system . This approach of fers numerous benefits , with the most signi ficant being the predominantly exclusive illumination of the detection system' s focal plane . This results in optical sectioning and minimal excitation of out-of- focus regions , ultimately yielding sharp images and signi ficantly reducing sample bleaching when compared to conventional microscopy techniques .

[0062] An ideal light sheet is characteri zed by a consistently minimal width over a substantial distance . Due to the fundamental physical constraints that inherently limit the resolution of any optical instrument , achieving this geometric ideal can only be approximated . In practical applications , astigmatic Gaussian beams , wherein a Gaussian beam i s focused through a cylindrical lens , are the prevailing choice for generating a light sheet . A better approximation of a sheet may be achieved by tiling a few Gaussian beams along the propagation axis . However, this method demands longer acquisition time and adds fluctuations to the overall beam width .

[0063] The disclosed systems and methods provide a simple and intuitive designing of a Superposition Gaussian Beam ( SGB ) with constant width and intensity along an extended propagation length, which better approximates an ideal light sheet .

[0064] The disclosed non-di f fracting Gaussian-like beams have a transverse Gaussian intensity profile , but unlike common Gaussian beams , in the longitudinal direction the profile is uni form and narrow along an extended propagation length .

[0065] The functionality of a lens is to map the entire input plane to a spot at the focal plane . Similar to an axicon, wherein each radius in the input plane is mapped to a different axial location to generate a focal line, superposing the transmission function of several lenses with different foci results in a mapping of the entire input plane to spots at different axial locations, generating an SGB. For example, superposing in this manner the functions of a set of cylindrical lenses with evenly spaced focal points results in a superposition lens that generates an astigmatic SGB (a light sheet) that has constant width and intensity for a much longer propagation distance than a regular (stigmatic or astigmatic) Gaussian beam.

[0066] The disclosed beam may be constructed using a superposition lens by applying a transmission function which is a superposition of transmission functions of lenses with different foci. The superposition of the transmission functions may be implemented on an optical phase modulator such as an SLM.

[0067] The present embodiments are able to produce both stigmatic and astigmatic superposition beams, either propagating along a straight line or accelerating, i.e., following a curved trajectory. Simulations were made demonstrating both stigmatic and astigmatic SGBs according to the disclosure. In addition, an acceleration of SGBs was also demonstrated, as will be detailed below.

[0068] The disclosed Superposition Gaussian Beams (SGBs) can be useful for a variety of applications, such as optical tweezing or trapping, direct laser writing (DLW) or materials processing. The properties of the astigmatic SGB may be highly useful for light sheet microscopy, in which constant width and intensity are of high importance. In embodiments described below, an SLM modulates a coherent laser beam with a novel modulation function that gives rise to an SGB. This modulation function causes the SLM to modulate a regular collimated Gaussian beam impinging on the SLM so that the beam reflected from the SLM has the form of an SGB, which may be stigmatic or astigmatic. A stigmatic SGB has a cylindrical symmetry, and its overall geometry is approximated by a line. An astigmatic SGB is a light sheet.

[0069] The modulation function that is applied by the SLM is a superposition of transfer functions of an array of regular single focus lenses. Each transfer function in the superposition realizes the focusing of a beam to a given single spot, whose distance from the SLM is characterized by a given focal length. The stigmatic SGB is created using a superposition of regular spherical lens transfer functions, whereas the astigmatic beam is created using a superposition of cylindrical lens transfer functions. For both types of SGB, the set of foci are equidistant along a line. The resulting SGB focuses light along a line in the stigmatic case and along a plane in the astigmatic case.

[0070] Numerical simulations, as further detailed below, show that SGBs have superior properties to regular beams (focused with a single simple lens) . SGBs remain in focus or substantially in focus (e.g., its on-axis intensity stays above 90% of its maximum value ) along much longer lengths (e.g., along up to 2.4 of the Rayleigh length) . Thus, the astigmatic SGB provides a superior light sheet for microscopy.

[0071] In some embodiments, the modulation function of the

[0072] SLM is chosen to realize an accelerating beam, i.e., a beam whose profile is bent , by distributing the set of foci along a curve in space , rather than along a line .

[0073] According to some aspects , the length of the disclosed beam L may be defined as the desired extension range of beam foci around an initial beam focus location f relative to the superposition lens . In other words , the superposition beam may be made of beams whose focal points cover the range between f - L / 2 to f + L / 2 .

[0074] Taking the asymptotic expression wherein the spacing between the foci of the superposed beams is very small , an expression for the transmission function of the superposition lens is received : where f is the central focal plane , L is the beam length, A is the wavelength, and Ei is the exponential integral function .

[0075] Taking the asymptotic expression in which the spacing between the foci of the superposed beams is very small an expression for the transmission function of the superposition beam for the stigmatic case may be received : (2)

[0076] To characterize the non-dif fraction properties of the SGB, three metrics are further disclosed. The first metric is Zwidth, which is the distance where the transverse width of the beam expands by 5% for the astigmatic case and 15% for the stigmatic case. The second is Zintensity, which is the distance over which the on-axis intensity of the beam is reduced to 90% of its peak value. The third is Symmetryrwhich is an estimation of the symmetry of the on-axis intensity around its center. Symmetry is defined as: where I (z) is the on-axis intensity of the beam, which leads to a value of 0 for a completely symmetric beam and for a value of 1 for a completely anti-symmetric beam.

[0077] According to some aspects, a spatial acceleration may be added to the SGB, by defining a trajectory for the optical axis of the beam. To realize the trajectory, each lens in the superposition may be shifted to a different transverse location or tilted in order to generate a curve in space. There is no analytical expression for the transmission function of the superposition beam in this case. Shifting or tilting each lens results in a transversely shifted focal spot, and their superposition results in a curved SGB when a Gaussian beam illuminates the resulting transfer function. This may apply for both stigmatic and astigmatic SGBs . According to some aspects, an accelerating SGB according to the disclosure may be used to bypass obstacles , which may be useful in the field of material processing in particular .

[0078] According to some aspects , an apparatus for optical proj ection according to the disclosure may include a light source and an optical phase modulator .

[0079] The light source may be configured to output a coherent beam of optical radiation . The optical phase modulator may be configured to modulate the beam with a spatial modulation profile including a superposition of respective trans fer functions of multiple lenses with di f ferent foci so as to generate a superposition Gaussian beam . According to some aspects , the optical phase modulator includes an SLM . According to some aspects , the optical phase modulator includes one or more di ffractive or refractive optical elements .

[0080] In other embodiments of the present invention, any suitable type of optical phase modulator can provide the spatial light modulation required to generate the SGB, operating in either a reflective or a transmissive mode . For example , the optical phase modulator may comprise a high-resolution liquid crystal on silicon ( LCOS ) SLM, of a type that is commercially available from several vendors . Alternatively, the optical phase modulator may comprise a static phase modulation element , such as an optical meta surface or a holographic grating, which is designed to implement the SGB trans fer function . All such alternative means for generating the SGB are considered to be within the scope of the present invention .

[0081] According to some aspects , each trans fer function of the superposition of trans fer functions reali zes the focusing of a beam to a given single spot or line, whose distance from the optical phase modulator is characterized by a given focal length.

[0082] According to some aspects, the transfer functions may correspond to spherical lenses, where the optical phase modulator generates a stigmatic SGB. According to some aspects, the ratio between the Rayleigh range of a beam realized by a transfer function having the middle focal length and the length of the SGB is between 0.06 and 0.22 (e.g., equal to or higher than 0.06 and equal to or lower than 0.22) to receive high beam quality.

[0083] According to some aspects, the transfer functions may correspond to cylindrical lenses, where the optical phase modulator generates an astigmatic SGB. According to some aspects, the astigmatic SGB may include a light sheet, to be directed to impinge on a sample in a light-sheet microscope. According to some aspects, the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of the transfer functions having the middle focal length and the length of the SGB is less than or equal to 0.09 and more than or equal to 0.04, to receive high beam quality.

[0084] According to some aspects, the non-dif fraction properties of the generated SGB may be characterized by the distance where the transverse width of the SGB expands by 5% (e.g., for the astigmatic case) , the distance at which the transverse width expands by a maximum of 15% (e.g., for the stigmatic case) , the distance over which the on-axis intensity of the SGB is reduced to 90% of its peak value, an estimation of the symmetry of the on-axis intensity around the center of the SGB, or a combination thereof.

[0085] According to some aspects, the SGB propagates along a straight line. The different foci may then be equidistant along a line. According to some aspects, the SGB follows a curved trajectory.

[0086] According to some aspects, a light-sheet microscope which includes or integrates the disclosed apparatus is further disclosed. Such a microscope is shown, for example, in FIG. 1. The disclosed apparatus is then used to generate an astigmatic SGB including a light sheet, to be directed to impinge on a sample.

[0087] Fig. 1 shows an exemplary optical scheme 100 which may be used to generate SGB illumination in a light-sheet microscope. A coherent beam of optical radiation 180 enters a beam splitter 120. The beam is generated by a light source (not shown) . A portion of beam 180 then enters an optical phase modulator 110, which in this example is a reflective SLM. A modulated beam or SGB 180A is then returned to beam splitter 120. A portion of SGB 180A, SGB 180B, is then output towards lenses 130 and 140. According to some aspects, beam splitter 120 may be removed such that beam 180 enters SLM 110 directly and then output from SLM 110 directly towards lens 130. Beam splitter 120 may allow a more compact layout. SGB 180B may be imaged and resized by lenses 130 and 140 having a shared focal plane 135 to generate a light-sheet beam 180C for illuminating a sample located at a plane indicated by line 145. The light emanating from the sample, e.g., beam 180D, is imaged by lenses 150 and 160 through a shared focal plane 155 to generate beam 180E which then enters a camera 170 (e.g., a Complementary Metal Oxide Semiconductor (CMOS) camera) .

[0088] According to some aspects, the elements which are shown in FIG. 1 may be included in or form a light-sheet microscope. According to some aspects, a light source (not shown) and SLM 110 may be or may form an apparatus for optical projection according to the disclosure which may be coupled with or integrated into a light-sheet microscope. SLM 110 of FIG. 1 may be operated according to the disclosed methods, such as method 200 of FIG. 2.

[0089] Reference is now made to FIG. 2, which shows a flow diagram of a method 200 for optical projecting. Method 200 may be applied via the apparatuses of the disclosure, via the scheme of FIG. 1 or by one or more of the optical elements or devices shown in FIG. 1. Method 200 will be further described with respect to FIG. 1.

[0090] At a step 230, a projected coherent beam of optical radiation may be modulated with a spatial modulation profile comprising a superposition of respective transfer functions of multiple lenses with different foci so as to generate a superposition Gaussian beam (SGB) . According to some aspects, the modulation may be performed by an optical phase modulator, e.g., an optical phase modulator of the disclosed apparatus, such as SLM 100 of FIG. 1. According to some aspects, the modulating of the beam is performed via one or more diffractive or refractive optical elements.

[0091] According to some aspects, each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single spot or line, whose distance from the optical phase modulator is characterized by a given focal length. According to some aspects, the transfer functions correspond to spherical lenses . Generating the SGB may then include generating a stigmatic SGB. According to some aspects, the modulation is performed such that the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is more than or equal to 0.06 and less than or equal to 0.22 for high beam quality.

[0092] According to some aspects, the transfer functions correspond to cylindrical lenses. Generating the SGB may then include generating an astigmatic SGB. According to some aspects, the astigmatic SGB includes a light sheet, such as light sheet 180C of FIG. 1. Method 200 may then further include an optional step 240 according to which the SGB is directed to impinge on a sample in a light-sheet microscope, as shown, for example, in FIG. 1. According to some aspects, the modulation may be performed such that the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is less than or equal to 0.09 and more than or equal to 0.04 for high beam quality.

[0093] At an optional step 220, the coherent beam may be projected, e.g., by a light source of the disclosed apparatus .

[0094] At an optional step 210, the superposition of respective transfer functions may be calculated or determined. According to some aspects, the superposition of respective transfer functions may be calculated based on the disclosed asymptotic expressions. According to some aspects , method 200 may further include an optional step of characteri zing the nondi f fraction properties of the generated SGB by the distance where the transverse width of the SGB expands by 5% , the distance at which the width expands by a maximum of 15% , the distance over which the on-axis intensity of the SGB is reduced to 90% of its peak value , an estimation of the symmetry of the on-axis intensity around the center of the SGB, or a combination thereof .

[0095] According to some aspects , the modulation may be performed such that the SGB propagates along a straight line . According to some aspects , the modulation may be performed such that the di f ferent foci are equidistant along a line . According to some aspects , each lens of the multiple lenses is shi fted to a di f ferent transverse location or tilted such that the SGB follows a curved tra j ectory .

[0096] According to some aspects , one or more steps of method 200 may be performed or may be caused by one or more controllers . According to some aspects , the modulation of step 200 may be performed or may be caused by at least one controller . According to some aspects , additional one or more steps of optional steps 210 , 220 , 240 or any other step of method 200 may be performed or may be caused by the at least one controller .

[0097] A computer program product is further disclosed . The computer program product includes a computer-readable storage medium having computer-executable instructions . The computer-executable instructions may include instructions for modulating a proj ected coherent beam of optical radiation with a spatial modulation profile including a superposition of respective trans fer functions of multiple lenses with di f ferent foci so as to generate an SGB . According to some aspects , the trans fer functions may correspond to spherical lenses , so as to generate a stigmatic SGB . According to some aspects , the trans fer functions may correspond to cylindrical lenses , so as to generate an astigmatic SGB .

[0098] According to some aspects , the instructions may include instructions for applying method 200 .

[0099] RESULTS OF SIMULATIONS

[0100] ASTIGMATIC SGB - A LIGHT SHEET

[0101] Several cylindrical lenses ( 103 ) were superposed to generate an astigmatic SGB . A transmission function was calculated and proj ected onto a modulating device such that when it is illuminated with a Gaus sian beam, it results in a superposition o f astigmatic Gaus sian beams with di f ferent waist locations . For better results , the resolution of spacing between the foci of the lenses was empirically chosen to be smaller than or equal to a quarter of the Rayleigh range of the beam with the shortest focal distance . Below this limit , the beam may not change any more , while above this limit the beam may exhibit some longitudinal oscillations .

[0102] Following the guideline mentioned above for proper spacing between foci of the superposed beams to generate the SGB led to results that are virtually indistinguishable from the ones given by the analytical expression . Reference is now made to FIG. 3, which shows graphs 300A-300C presenting an astigmatic SGB in comparison to an astigmatic Gaussian beam. Graph 300A shows a beam width along the propagation of a Gaussian beam (indicated by a dotted line) and an SGB (indicated by a continuous line) . Graph 300B shows normalized on axis intensity along the propagation of a Gaussian beam (indicated by a dotted line) and an SGB (indicated by a continuous line) . Graph 300C shows on axis phase along the propagation of a Gaussian beam (indicated by a dotted line) and an SGB (indicated by a continuous line) .The SGB light sheet and the Gaussian light sheet have the same waist, while the ratio between the Rayleigh range of the beam with the middle focal length in the superposition (e.g., having a focal length value which is in the middle or substantially in the middle with respect to all the focal values of the beams realized by the transfer functions generating the superposition) , ZRO, to the superposition beam length L is 0.0549. The transverse coordinates are normalized by the waist of the Gaussian beam , and the axial coordinate is normalized by its Rayleigh range ZR. ZRO is the Rayleigh range of the beam with the middle focal length in the superposition, and ZR is the Rayleigh range of a Gaussian beam with the same waist as the SGB. The aperture size in the simulations was 137wo x llwo. In this example, twice the Rayleigh range of the longest beam in the superposition is shorter by a factor of 6.8 compared to the overall length of the superposition beam. The Gouy phase is presented in FIG. 300C, in which one can see a slight difference between the two beams. FIGS. 300A and 300B demonstrate the significant improvement in the non-dif fraction properties of the SGB relative to a Gaussian beam.

[0103] Reference is now made to FIG. 4, which shows graphs 400A-400E presenting the MTFs of the astigmatic SGB in comparison to the astigmatic Gaussian beam of FIG. 3 at different planes along propagation direction. Graphs 400A and 400B show the MTFs before the focal plane (e.g., the focal plane of a Gaussian and the central focal plane of the SGB) . Graph 400C shows the MTFs at the focal plane. Graphs 400D and 400E show the MTFs after the focal plane. ZR is the Rayleigh range of the Gaussian beam with the same waist as the SGB. The ratio of ZR / L here is 0.0549. Graph 400C shows the MTFs at the focal plane, where the beams are similar. Graphs 400B and 400D show the MTFs at a similar distance from the focal plane, and it can be seen that the MTF of the SGB is much wider. It remains wider even farther from the focal plane, as seen in Graphs 400A and 400E.

[0104] Calculating the disclosed metrics for the beam of FIG. 3, provides that Zwidth ,SGB — 2.86 Zwidth , Gauss and Zin tensi ty , SGB — 2.36 x Zintensity, Gauss as may be seen in Graphs 300A and 300B.

[0105] These metrics were numerically calculated for many different beams as a function of the ratio ZRO / L. According to some aspects, the ratio ZRO / L may be less than or equal to 0.09 and more than or equal to 0.04 to achieve better results .

[0106] STIGMATIC SGB

[0107] To generate a stigmatic SGB, several stigmatic (e.g., spherical) lenses were superposed. When such a transmission function is illuminated with a Gaussian beam, it results in a superposition of stigmatic Gaussian beams with different waist locations. For better results, the resolution of spacing between the foci of the lenses was empirically chosen to be smaller than or equal to half of the Rayleigh range of the beam with the shortest focal distance. Here, Zwidth is the distance at which the width expands by a maximum of 15% (which is different from the metric used for the astigmatic beam) , since the beam is a bit less uniform than in the astigmatic case.

[0108] Reference is now made to FIG. 5, which includes graphs 500A-500C presenting a stigmatic SGB in comparison to a stigmatic Gaussian beam that has the same waist. Graph 500A shows beam width along propagation of a Gaussian beam (indicated by a dotted line) and an SGB (indicated by a continuous line) . Graph 500B shows normalized on axis intensity along propagation of a Gaussian beam (indicated by a dotted line) and an SGB (indicated by a continuous line) . Graph 500C shows on axis phase along propagation of a Gaussian beam (indicated by a dotted line) and an SGB (indicated by a continuous line) .

[0109] Calculating for the beam in FIG. 5, it was received that Zwidth , SGB = 1.69 X Zwidth , Gauss and Zintensity,SGB = 2.29 X Zintensity, Gauss as can be seen in graphs 500A and 500B.

[0110] These metrics were also calculated for many beams, each characterized by a specific ratio of ZR / L. According to some aspects, ZRO / L may be less than or equal to 0.22 and more than or equal to 0.06 to achieve better results. Here, as in the astigmatic case, following the guideline mentioned above for proper spacing between foci of the superposed beams to generate the stigmatic SGB led to results that are virtually indistinguishable from the ones given by the analytical expression. The ratio of ZRO / L here is 0.2112. Again, the transverse coordinates are normalized by the waist of the Gaussian beam, and the axial coordinate is normalized by its Rayleigh range. The aperture size in the simulations was 77wo x llw . Graphs 500A and 500B show the significant improvement in the non-dif fraction properties of the SGB relative to a Gaussian beam. The Gouy phase is presented in graph 500C, and one can see a slight difference between the two beams .

[0111] The disclosed controller may be or may include, for example, one or more central processing unit processor (s) (CPU) , one or more Graphics Processing Unit(s) (GPU or GPGPU) , and / or other types of processors, such as a microprocessor, digital signal processor, microcontroller, programmable logic device (PLD) , field programmable gate array (FPGA) , or any suitable computing or computational device .

[0112] The disclosed computer-readable storage medium may be or may include, for example, one or more of a hard disk drive, a solid-state drive, an optical disc drive, a USB drive or other removable storage device, and / or other types of removable or non-removable storage devices. Data such as instructions, code, procedure data, among other things, may be stored in the storage and may be loaded from storage into memory, where it may be processed by a controller.

[0113] Throughout the specification discussions utilizing terms such as "calculating", "processing," "computing," "storing," "determining," or the like with respect to a controller or a hardware processor, refer to the action and / or processes of a computer or computing system, or similar electronic computing device, that manipulate and / or trans form data represented as physical , such as electronic, quantities within the computing system ' s registers and / or memories into other data similarly represented as physical quantities within the computing system ' s memories , registers or other such information storage , transmission or display devices .

[0114] The embodiments described above are cited by way of example , and the present invention is not limited to what has been particularly shown and described hereinabove . Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove , as well as variations and modi fications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art .

Claims

CLAIMS1. Apparatus for optical projection, comprising: a light source, which is configured to output a coherent beam of optical radiation; and an optical phase modulator, configured to modulate the beam with a spatial modulation profile comprising a superposition of respective transfer functions of multiple lenses with different foci so as to generate a superposition Gaussian beam (SGB) .

2. The apparatus according to claim 1, wherein the transfer functions correspond to spherical lenses, whereby the optical phase modulator generates a stigmatic SGB.

3. The apparatus according to claim 2, wherein each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single spot, whose distance from the optical phase modulator is characterized by a given focal length.

4. The apparatus according to claim 3, wherein the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is more than or equal to 0.06 and less than or equal to 0.22.

5. The apparatus according to claim 3, wherein the resolution of spacing between the foci of the multiple lenses is smaller than or equal to half of the Rayleigh range of the beam with the shortest focal distance realized by a transfer function of the superposition of transfer functions .

6. The apparatus according to claim 1, wherein the transfer functions correspond to cylindrical lenses, whereby the optical phase modulator generates an astigmatic SGB. . The apparatus according to claim 6, wherein the astigmatic SGB comprises a light sheet, to be directed to impinge on a sample in a light-sheet microscope.

8. The apparatus according to claim 6, wherein each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single line, whose distance from the optical phase modulator is characterized by a given focal length.

9. The apparatus according to claim 8, wherein the modulation is performed such that the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is less than or equal to 0.09 and more than or equal to 0.04.

10. The apparatus according to claim 8, wherein the resolution of spacing between the foci of the multiple lenses is smaller than or equal to a quarter of the Rayleigh range of the beam with the shortest focal distance realized by a transfer function of the superposition of transfer functions .

11. The apparatus according to any of claims 1-10, wherein the SGB propagates along a straight line.

12. The apparatus according to claim 11, wherein the different foci are equidistant along a line.

13. The apparatus according to any of claims 1-10, wherein the SGB follows a curved trajectory.

14. The apparatus according to any of claims 1-10, wherein the optical phase modulator comprises a spatial light modulator (SLM) .

15. The apparatus according to any of claims 1-10, wherein the optical phase modulator comprises one or more diffractive or refractive optical elements.

16. A method for optical projection, comprising modulating a projected coherent beam of optical radiation with a spatial modulation profile comprising a superposition of respective transfer functions of multiple lenses with different foci so as to generate a superposition Gaussian beam (SGB) .

17. The method according to claim 16, further comprising projecting the beam.

18. The method according to claim 16, further comprising calculating the superposition of respective transfer functions .

19. The method according to claim 16, wherein the transfer functions correspond to spherical lenses, and wherein generating the SGB comprises generating a stigmatic SGB.

20. The method according to claim 19, wherein each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single spot, whose distance from the optical phase modulator is characterized by a given focal length.

21. The method according to claim 20, wherein the modulation is performed such that the ratio between theRayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is less than or equal to 0.22 and more than or equal to 0.06.

22. The method according to claim 20, wherein the resolution of spacing between the foci of the multiple lenses is smaller than or equal to half of the Rayleigh range of the beam with the shortest focal distance realized by a transfer function of the superposition of transfer functions .

23. The method according to claim 16, wherein the transfer functions correspond to cylindrical lenses, wherein generating the SGB comprises generating an astigmatic SGB.

24. The method according to claim 23, wherein the astigmatic SGB comprises a light sheet, and wherein the method further comprises directing the SGB to impinge on a sample in a light-sheet microscope.

25. The method according to claim 23, wherein each transfer function of the superposition of transfer functions realizes the focusing of a beam to a given single line, whose distance from the optical phase modulator is characterized by a given focal length.

26. The method according to claim 23, wherein the modulation is performed such that the ratio between the Rayleigh range of a beam realized by a transfer function of the superposition of transfer functions having the middle focal length and the length of the SGB is less than or equal to 0.09 and more than or equal to 0.04.

27. The method according to claim 23, wherein the resolution of spacing between the foci of the multiple lenses is smaller than or equal to a quarter of the Rayleigh range of the beam with the shortest focal distance realized by a transfer function of the superposition of transfer functions .

28. The method according to claim 16, wherein the modulating of the beam is performed via a spatial light modulator (SLM) .

29. The method according to claim 16, wherein the modulating of the beam is performed via one or more diffractive or refractive optical elements.

30. The method according to any of claims 16-29, wherein modulation is performed such that the SGB propagates along a straight line.

31. The method according to claim 30, wherein the different foci are equidistant along a line.

32. The method according to any of claims 16-29, wherein each lens of the multiple lenses is shifted to a different transverse location or tilted such that the SGB follows a curved trajectory.

33. A computer program product comprising a computer- readable storage medium having computer-executable instructions for modulating a projected coherent beam of optical radiation with a spatial modulation profile comprising a superposition of respective transfer functions of multiple lenses with different foci so as to generate a superposition Gaussian beam (SGB) .

34. The computer program product according to claim 33, wherein the transfer functions correspond to spherical lenses, so as to generate a stigmatic SGB.

35. The computer program product according to claim 33, wherein the transfer functions correspond to cylindrical lenses, so as to generate an astigmatic SGB.

36. The computer program product according to claim 35, wherein the astigmatic SGB comprises a light sheet, to be directed to impinge on a sample in a light-sheet microscope .

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