WO2021191717A1

WO2021191717A1 - Single-shot astigmatic phase retrieval laser wavefront sensor and method

Info

Publication number: WO2021191717A1
Application number: PCT/IB2021/052091
Authority: WO
Inventors: Boon S. Ooi; Shuiqin ZHENG; Redha Hussein AL IBRAHIM; Tien Khee Ng
Original assignee: King Abdullah University Of Science And Technology
Priority date: 2020-03-24
Filing date: 2021-03-12
Publication date: 2021-09-30

Abstract

A single-shot astigmatic phase retrieval wavefront sensor system (100) includes a single 2-dimensional (2D) grating (110) configured to split an incoming optical beam (112) into plural split beams (114-I) and to modulate each of the plural split beams (114-I) with a corresponding modulation of plural modulations; a light sensor (120) configured to receive the plural split beams (114-I) and determine a light intensity of each of the plural split beams (114-I); and a processing unit (130) connected to the light sensor (120) and configured to calculate a phase distribution of a wavefront of the incoming optical beam (112) based on simultaneously measured light intensities of the plural split beams (114-I).

Description

SINGLE-SHOT ASTIGMATIC PHASE RETRIEVAL LASER WAVEFRONT

SENSOR AND METHOD

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 62/993,934, filed on March 24, 2020, entitled “SINGLE-SHOT ASTIGMATIC PHASE RETRIEVAL LASER WAVE-FRONT SENSOR,” the disclosure of which is incorporated herein by reference in its entirety.

BACKGROUND

TECHNICAL FIELD

[0002] Embodiments of the subject matter disclosed herein generally relate to the extraction of full optical wavefront information from an optical beam, and more particularly, to a sensor that is configured to extract both the intensity distribution and the phase distribution associated with the optical beam.

DISCUSSION OF THE BACKGROUND

[0003] An optical beam or signal, which may be generated by a laser device, is characterized by the optical or light intensity (i.e. , the amount of light that arrives on a given area per a given time unit) and also by the phase information (i.e., the phase or angle associated with the electrical field that is associated with the given optical signal). Traditional optical sensors only respond to light intensity, while the phase information (or wavefront data) is lost during the measurement process. Wavefront data having the phase information is useful and important. For example, it can be used for unlabeled transparent cell imaging, three-dimensional imaging of integrated circuit, digital refocusing, adaptive optics and laser-quality analysis.

[0004] For acquiring the phase distribution or wavefront distribution, the existing methods can be divided into two types, according to the requirement of the reference light. One is the interference method, and the other is the non-interference method. For the interference method, it needs an additional light beam (a reference light beam) with a known wavefront distribution, and the system requires a high stability. In some applications, the reference light beam cannot be conveniently introduced, for example, in the underwater environment. For the non-interference wavefront reconstruction method, one way is to use some optical system to get the phase gradient, such as the beam shearing method and Shack-Hartmann wavefront sensor. Getting the phase gradient with these methods need an integration operation to obtain the phase. However, a different integral path will lead to a different integral phase when the field has phase singularity.

[0005] Another way is to use a diffraction pattern to reconstruct the wavefront information. The lost phase can be retrieved through phase retrieval algorithms. However, it is important to note that the loss of phase information during detection may result in the same diffraction patterns corresponding to multiple physically different structures. It means that the uniqueness of the reconstruction cannot be guaranteed. Phase diversity is a method to further ensure uniqueness, which requires a focused image and a defocused image. However, this method cannot distinguish light with a circular symmetry intensity distribution and chiral phase distribution, such as an optical vortex.

[0006] To guarantee the uniqueness of wavefront recovery, the astigmatic phase retrieval was proposed [1] Note that the term “astigmatic” is used herein to refer to an aberration of a lens or other optical system due to which the image of a point is spread out along the axis of the system. The astigmatic phase retrieval needs at least three diffraction patterns with different phase modulations. Thus, the most primitive astigmatic phase retrieval system needs to capture three different patterns, for example, (1) one with the field under horizontal curvature phase modulation, (2) one with no curvature modulation, and (3) one with a vertical curvature phase modulation [2], and such system requires switching of optical elements to achieve the three modulations. Such a system is cumbersome and prone to failure due to the switching requirement.

[0007] To solve the problem of component switching, an astigmatic phase retrieval method with a spatial light modulator (SLM) was proposed [3] This method uses the SLM to act as different optical elements. Then, the patterns for the various modulations can be captured without any moveable optical elements, only by changing the modulation on the SLM. This system can conveniently load more phase modulations to obtain more diffraction patterns to increase the convergence speed of the wavefront recovery. However, for this technology, an SLM is indispensable, which needs complicated calibration for a 2p phase shift and compensation for wavefront flatness, notwithstanding the high cost of this implementation. [0008] To induce more modulation without the SLM, another astigmatic phase retrieval method with a rotatable cylindrical lens was proposed [4] However, all these improved system need phase modulation switching, which is prone to failure. Thus, all these astigmatic phase retrieval methods are still a multi-shot measurement technology because the diffraction patterns acquisition needs several shots for achieving them, i.e. , repetition. For the case when the optical field is changing faster than the phase modulation switching, these technologies do not work correctly because the measured fields are not the same.

[0009] Thus, there is a need for a novel technology that is capable to acquire several diffraction patterns with different phase modulations in a single-shot measurement, through which the astigmatic phase retrieval can be realized in single shot measurement.

BRIEF SUMMARY OF THE INVENTION

[0010] According to an embodiment, there is a single-shot astigmatic phase retrieval wavefront sensor system that includes a single 2-dimensional (2D) grating configured to split an incoming optical beam into plural split beams and to modulate each of the plural split beams with a corresponding modulation of plural modulations; a light sensor configured to receive the plural split beams and determine a light intensity of each of the plural split beams; and a processing unit connected to the light sensor and configured to calculate a phase distribution of a wavefront of the incoming optical beam based on simultaneously measured light intensities of the plural split beams.

[0011] According to another embodiment, there is a method for reconstruction of a wavefront of an optical beam, and the method includes receiving a coherent light beam having a random, non-zero, wavefront distribution L(x,y), where x and y are Cartesian coordinates of a plane; phase modulating the coherent light beam with a preset phase modulation function Ø(x,y) of a single, 2-dimensional (2D) grating, to obtain a modulated coherent field M(x, y), wherein the modulated coherent field M(x, y) includes plural split beams, each modulated with a different modulation corresponding to the preset phase modulation function Ø(x,y); calculating a coherent field D(x, y) on a plane of an optical sensor, wherein the coherent field D(x, y) corresponds to the modulated coherent field M(x, y); calculating with a processing unit a modulus constrained field D’(x, y), by imposing a modulus constraint on (1) a phase of the coherent field D(x, y) and (2) an intensity l(x, y) of the plural split beams, which is measured by the optical sensor; calculating an error between the coherent field D(x, y) and the modulus constrained field D’(x, y); backward propagating the modulus constrained field D’(x, y) to calculate a backward propagation coherent field distribution M’(x, y); calculating a reversed coherent field L’(x, y) based on the backward propagation coherent field distribution M’(x, y); and outputting the reversed coherent field L’(x, y) as the reconstructed wavefront of the optical beam when the error is smaller than a present threshold.

[0012] According to yet another embodiment, there is a non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a computer, implement the method discussed above.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:

[0014] Figure 1 is a schematic diagram of a single-shot astigmatic phase retrieval wavefront sensor device;

[0015] Figure 2A illustrates plural split beams generated by a traditional grating having straight ridges, Figure 2B illustrates plural split beams generated by a grating having curved ridges, Figure 2C illustrates plural split beams generated by a grating having a combination of straight ridges that are perpendicular to each other, and Figure 2D illustrates a grating that combines curved ridges with different orientations to apply different modulations to the split beams;

[0016] Figure 3 illustrates an embodiment of a single 2D grating that achieves simultaneously six different modulations for a single incoming optical beam;

[0017] Figure 4 shows a schematic diagram of a single-shot astigmatic phase retrieval wavefront sensor device for a macro wavefront;

[0018] Figure 5 shows a schematic diagram of a single-shot astigmatic phase retrieval wavefront sensor device for a micro wavefront;

[0019] Figure 6 is a flow chart of a method for retrieval of a phase of a wavefront of an optical beam; and [0020] Figure 7 schematically illustrates the various fields that are measured or calculated for retrieving the phase of the wavefront of an optical beam.

DETAILED DESCRIPTION OF THE INVENTION

[0021] The following description of the embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. The following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. The following embodiments are discussed, for simplicity, with regard to a grating having six different patterns for splitting an incoming optical beam and modulating each split beam with a different phase modulation. However, the embodiments to be discussed next are not limited to a grating with six different patterns, but may be applied to any number of different patterns.

[0022] Reference throughout the specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with an embodiment is included in at least one embodiment of the subject matter disclosed. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” in various places throughout the specification is not necessarily referring to the same embodiment. Further, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments.

[0023] According to an embodiment, a single-shot astigmatic phase retrieval sensor system 100, as shown in Figure 1, is configured to simultaneously detect the light intensity and the phase information of an incoming optical beam by using a single shot approach. The single-shot astigmatic phase retrieval sensor system 100 includes a 2-dimensional (2D) grating 110, which is manufactured to split an incoming optical beam 112 into M x N beams 114-1, with I being an integer equal to M x N, where each beam is modulated by a superposition of two or more independent grating patterns. The 2D grating 110 is a single grating in this embodiment, i.e. , a single piece of material that provides the modulation of the plural split optical beams 114-1. A single surface of the 2D grating 110 is manufactured, as discussed later, to achieve the two or more independent patterns. In one application, the single surface of the 2D grating 110 can implement six different patterns (see Figure 3).

[0024] The single-shot astigmatic phase retrieval sensor system 100 also includes a sensor 120, which is capable of measuring a light intensity of the plural optical split beams 114-1. In one application, the light intensities of the plural split beams are simultaneously recorded in a single plane of the sensor 120.

[0025] The system 100 further includes a processing unit 130, which is electrically connected to the sensor 120, and the processing unit 130 may store software commands that are capable of recreating the phase information of the incoming optical beam 112 from the measured split beams due to the 2D grating. The system 100 may also include a power supply 140, for example, a battery, which is configured to supply electrical power to the processing unit 130 and the sensor 120. In one application, the system 100 may also include a communication interface 150, which is configured to communicate with an external device 190, which may be a smart device, a computer, a server, a cell tower, etc. The components 110 to 150 may be placed within a housing 160 for protecting them from the environment. The housing 160 may have or more openings 162 or a transparent part so that the incoming optical beam 112 can reach the 2D grating 110. The various components of the single-shot astigmatic phase retrieval sensor system 100 are now discussed with regard to the figures.

[0026] The component of the single-shot astigmatic phase retrieval sensor system 100 that splits the incoming optical beam 112 into the plural beams 114-1 and modulates each one according to a predetermined pattern is the 2D grating 110. In one application, no property (i.e., position, speed, shape) of the single 2D grating is changed during the operation of the system. Before discussing in more detail the structure and effects of the 2D grating 110, a short introduction to the properties of a traditional grating is believed to be in order. A phase grating refers in the art to a device that introduces a spatial periodic phase modulation of an incoming optical beam. A periodic function g(2π ^. f ^. x) can be used to represent the phase modulation of this grating, where f is the spatial frequency and x is the spatial variable. A diffraction beam splitting grating 210, which is shown in Figure 2A, is known to be a slab of plastic or glass or any other transparent material that has plural parallel ridges or grooves 212 formed into one of its surface. When the incoming optical beam 112 is shone perpendicular on this surface, the beam passes through the grating and splits into N beams 114-1 to 114-3, where N is the order of the beam. Figure 2A shows for simplicity only 3 beams. For this case, the periodic function g_N describes the periodic phase modulation of the generated beams. Each beam has a different propagation direction, which depends on the period of the ridges made into the surface of the grating, and the wavelength of the incident optical beam. For the diffraction beam splitting grating, the parallel ridges are extending along straight lines. Figure 2A also shows a cross-section 214 of the incoming optical beam 112 and a cross-section 216 of the resulting split beams 114- I .

[0027] However, a grating 220 may be manufactured to have curved ridges 222, as shown in Figure 2B, which will add a spatial phase φ (x,y ), for example, a converging spherical phase, to the periodic function g_N, which results in a new periodic function g_N(2πf_xx + φ (x,y )). For this case of grating, each diffractive beam 114-1 will have an additional phase n * φ (x,y ), where n is the diffraction order. The curved ridges introduce this additional phase shift to each order, except the zero order, which does not change. As noted in Figure 2B, the additional phase shift influences the cross-section 216 of each split beam 114-1, i.e. , its cross-section is modulated by the phase shift and the phase is described by _e ^{inφ( x}’^y), which makes the positive orders to have a converging spherical phase and the negative orders to have a diverging spherical phase.

[0028] Two gratings 210 and 210’ can be combined in a single 2D grating 230, as shown in Figure 2C, where the orientation of the ridges of the two gratings are perpendicular to each other. It is noted that the resulting cross-section 236 of the split beams generated by the 2D grating 230 is a combination of the cross-sections 216 and 216’ of the split beams resulting from the individual gratings 210 and 210’, respectively, in terms of the number 3x2 of the split beams, without affecting the size of the split beams’ cross-section. It is noted that the resulting phase function becomes g_M(2πf_xx ) + g_N(2πf_yx), where the spatial frequencies f_x and f_y are now measured along perpendicular directions X and Y.

[0029] If two gratings 220 and 220’ having differently oriented curved ridges are now combined, as shown in Figure 2D, a curved orthogonal binary grating 110 is obtained having the phase function given by g_M(πnf_xx + φ_x(x,y)) + g_N(2πf_yx + φ _y(x,y)), and having a number M x N of split beams. It is noted that the resulting cross-section 206 of the split beams generated by the 2D grating 110 is a combination of the cross-sections 226 and 226’ of the split beams resulting from the individual gratings 220 and 220’, not only in terms of the number 3 x 2 of the split beams, but also in terms of the size of the split beams’ cross-section. This superposition of the phase dynamic results in an overall phase given by n * q>_x(x,y ) + m * <p_y(x,y). Using the 2D grating 110, the split beams are modulated differently from each other, due to the geometry and the angle of diffraction, so that the 2D grating 110 acts as a different device for each order of diffraction, which is different from all other orders. In fact, the 2D grating 110 shown in Figure 2D achieves simultaneous individual split beam modulations without replacing any optics component, or rotating any component, or without using the expensive and unstable SLM discussed in the background section. The 2D grating 110 is inexpensive and stable, and does not have any moving parts, which make it less prone to failure.

[0030] Thus, for the case when combining into a single grating a M = 3 grating with curvature φ_c, m = [1, 0, -1] order splitting and N = 2 grating with curvature φ_y, n = [1, -1] order splitting, the resulting 2D grating 110 will split the incoming light beam into 3 x 2 orders with the following simultaneous phases:

[0031] For this case, if the angular phases are defined in terms of the positions x and y along the surface of the grate, for example, as f_c = π (x² - y²)/ (fλ) and φ_y = π(X² + y²)/(fλ), then the phase modulation of each order of the 3 x 2 orders of the grating 110 are as illustrated in the table of Figure 3. This means that with a same physical grating 110, each order of the split beams is differently modulated from the other orders with a single shot. In other words, this plural modulation of the plural split beams is achieved simultaneously with the 2D grating 110, in a single shot, i.e. , by shining only once the incoming optical beam 112 onto the grating.

[0032] Returning to Figure 1, a distance D between the 2D grating 110 and the sensor 120 needs to be selected so that the split beams 114-1 are separated by a distance S from each other when interacting with the sensor 120. The separation distance S depends on the sensitivity of the sensor 120. For example, if the pixel separation is s for a given sensor 120, the separation distance S should be about s.

In one application, the distance D is calculated to achieve this target. However, in some situations the distance D that would achieve S = s is quite large, in the order of cm. Thus, it is possible to use additional optics for separating the split optical beams 114-1 so that the distance D is reduced. As illustrated in Figure 4, optics 400 may be added upstream the 2D grating 110, so that the incoming optical beam 112 enters first the optics 400 and then the 2D grating 110. The optics 400 may be a convex lens having a focal length f, for which case the sensor 120 should be placed at the focal length point of the lens 400. This is the case when the front of the incoming beam 112 is very large, i.e., a macro-wavefront. In one application, the optics can be placed downstream relative to the 2D grating.

[0033] In one embodiment, a combination of lenses may be used if needed. For example, it is possible that the incoming optical beam 112 has a micro wavefront, i.e., a transverse cross-section of the beam is very small. In this case, as shown in Figure 5, it is possible to use a microscope objective or a divergent lens 410 to increase the cross-section of the optical beam 112 so that a larger optical beam 113 is achieved, and then to send the larger optical beam 113 to the lens 402 (optics 400 in Figure 4) as discussed in the embodiment of Figure 4. The additional lens 410 may be part of the optics 400. The focal distances of the lenses 402 and 410 are selected so that the distance D is in the cm or mm range.

[0034] The astigmatic phase retrieval method implemented for the system 100 is now discussed in more detail. As discussed with regard to Figure 3, the incoming laser beam 112 is passed first through the 2D grating 110, which applies a different phase modulation for each split beam 114-1 at a same time, and the corresponding diffraction patterns are recorded with the sensor 120 and the processing device 130. The sensor 120 may be a complementary metal-oxide-semiconductor (CMOS) or a charge-coupled device (CCD) sensor. From the patterns recorded by the sensor, the optical wavefront of the incoming optical beam can be recovered. [0035] As shown in Figure 3, the 2D grating 110 may be configured so that the phase modulation of each order can be expressed as: (1) a convex cylindrical lens whose axis is along the X-direction, (2) a convex lens, (3) a convex cylindrical lens whose axis is along the Y-direction, (4) a concave cylindrical lens whose axis is along Y-direction, (5) a concave lens, and (6) a concave cylindrical lens whose axis is along the X-direction. Based on this configuration of the grating, it is possible to realize the single-shot astigmatic phase retrieval.

[0036] Note that the recovery algorithm does not need any change if the micro wavefront is placed at the front focal plane of the microscope objective as shown in Figure 5, the photoelectric sensor is placed at the back focal plane of the lens, and the distance between the microscope objective and the photoelectric sensor is the sum of the two focus lengths.

[0037] The recovery algorithm is now discussed with regard to Figures 6 and 7. According to an embodiment, the method starts in step 600, by receiving, at the 2D grating 110, a coherent light beam L(x,y), which has a random, non-zero, wavefront distribution, where the x and y are the Cartesian coordinates of a 2D plane of the 2D grating 110. Note that a coherent light beam is understood in this embodiment to include two or more light rays that have the same frequency and waveform, and their phase difference is constant. Such a coherent light beam can be generated, for example, by a laser device. In step 602, the coherent light beam L(x,y) is phase modulated by the 2D grating 110, according to a preset phase modulation function Ø(x,y). The resulting optical beam is a modulated coherent field M(x,y). In this embodiment, the modulated beam M(x,y) is obtained as follows: In this embodiment, the phase modulation function Ø(x,y)

is the grating phase modulation function illustrated in Figure 3. However, other modulation functions may be used as long as each split beam is modulated differently from the other split beams in a single shot.

[0038] In step 604, a coherent field D(x,y) is calculated on the photoelectric sensor 120’s plane, based on the modulated field M(x,y). If the configuration of the system 100 shown in Figure 1 is used, the coherent field D(x,y) is given by:

where X is the wavelength of the incoming optical beam, D is the distance between the sensor 120 and the grating 110, k_x and k_y are the spatial angular frequencies along the x- and y-directions, F is the Fourier transformation, and F^-1 is inverse Fourier transformation. If the configuration of the system 100 shown in Figure 4 is used, i.e. , the macro wavefront system, then the coherent field D(x,y) at the sensor 120 is given by:

where and f is the focal length of the used lens

402. If the configuration of the system 100 shown in Figure 5 is used, i.e., the micro wavefront system, then the coherent field D(x,y) at the sensor 120 is given by:

where D is the distance between the photoelectric sensor and the grating, k_x and k_y are the spatial angular frequencies along the x- and y-directions, F is the Fourier transformation, and (x₂y2)= ( x1,y1)f2/f1 , where fi is the focal length of the used lens 402 and f₂ is the focal length of the microscope objective 410.

[0039] Next, in step 606, the modulus constraint [5] is used to obtain the modulus constrained field D'(x,y). In one application, the modulus constrained field is calculated with the processing unit 130 as follows: D'(x,y ) = , where I(x, y)

is the intensity distribution captured by the sensor 120, and is the phase of the field D(x,y).

[0040] In step 608 an error e is calculated with the processing unit 130, and this error represents the difference between the coherent field D(x,y ) at the sensor and the modulus constrained field D'(x,y). In one application, the calculation formula for the error is as follows: , where the double integral

of the square of the norm between is calculated over the plane of

the sensor 120.

[0041] In step 610, a backward propagation coherent optical field distribution M'(x,y) is calculated with the processing unit 130, based on the diffraction theory, from the modulus constrained field D'(x,y), as follows. For the configuration illustrated in Figure 1, M'(x,y) is given by:

[0042] For the macro wavefront system illustrated in Figure 4, M'(x,y) is given by:

[0043] For the micro wavefront system shown in Figure 5, M'(x,y) is given by:

[0044] In step 612, a reverse coherent field L'(x,y) is calculated with the processing unit 130, before modulation, based on the phase modulation function 0(x,y) and the optical field distribution M'(x,y). In one application, the optical field distribution M'(x,y) is calculated as follows:

[0045] In step 614, a filter is applied to the reverse coherent field L'(x, y) with a low-band, and the filtered field is used to replace the coherent light beam L(x,y), as schematically illustrated in Figure 7. The calculation formula for this step is:

where LBF is a function of the low-band filter in the spatial-frequency domain.

[0046] In step 616, if the error calculated in step 608, between the coherent field D(x,y) and the modulus constrained field D'(x,y), is greater than a preset value, the algorithm returns to step 602. Otherwise, the filtered field L'(x,y) is the final recovery wavefront and is output at step 618.

[0047] The method discussed above can be implemented in the system 100, more specifically, the processing unit 130, to detect not only the light intensity but also the phase distribution of an optical beam that is associated, for example, with transparent cell imaging, three-dimensional imaging of an integrated circuit, digital refocusing, adaptive optics, and laser-quality analysis.

[0048] The disclosed embodiments provide an astigmatic phase retrieval laser wavefront sensor system that is capable to determine the phase of a wavefront of a laser beam with a single shot. It should be understood that this description is not intended to limit the invention. On the contrary, the embodiments are intended to cover alternatives, modifications and equivalents, which are included in the spirit and scope of the invention as defined by the appended claims. Further, in the detailed description of the embodiments, numerous specific details are set forth in order to provide a comprehensive understanding of the claimed invention. However, one skilled in the art would understand that various embodiments may be practiced without such specific details.

[0049] Although the features and elements of the present embodiments are described in the embodiments in particular combinations, each feature or element can be used alone without the other features and elements of the embodiments or in various combinations with or without other features and elements disclosed herein. [0050] This written description uses examples of the subject matter disclosed to enable any person skilled in the art to practice the same, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims.

References

[1] Nugent, K. A., et al. "Unique phase recovery for nonperiodic objects." Physical review letters 91.20 (2003): 203902.

[2] Henderson, Clare A., et al. "Astigmatic phase retrieval: an experimental demonstration." Optics express 17.14 (2009): 11905-11915.

[3] Rodrigo, Jose A., et al. "Wavefield imaging via iterative retrieval based on phase modulation diversity." Optics express 19.19 (2011): 18621-18635.

[4] Zheng, Shuiqin, et al. "Coherent diffractive imaging via a rotatable cylindrical lens." Optics and Lasers in Engineering 124 (2020): 105820.

[5] Pollefeys, Marc, et al. “The modulus constraint: a new constraint for self-calibration.” Conference: Pattern Recognition, 1996, Proceedings of the 13^th International

Conference on Volume 1.

Claims

WHAT IS CLAIMED IS:

1. A single-shot astigmatic phase retrieval wavefront sensor system (100) comprising: a single 2-dimensional (2D) grating (110) configured to split an incoming optical beam (112) into plural split beams (114-1) and to modulate each of the plural split beams (114-1) with a corresponding modulation of plural modulations; a light sensor (120) configured to receive the plural split beams (114-1) and determine a light intensity of each of the plural split beams (114-1); and a processing unit (130) connected to the light sensor (120) and configured to calculate a phase distribution of a wavefront of the incoming optical beam (112) based on simultaneously measured light intensities of the plural split beams (114-1).

2. The sensor system of Claim 1, wherein the plural modulations are applied by the single 2D grating in a single-shot of the incoming optical beam.

3. The sensor system of Claim 2, wherein properties of the single 2D grating are not changing.

4. The sensor system of Claim 1, wherein the single 2D grating extends in a plane defined by X- and Y-directions, and the single 2D grating is configured to have patterns associated with (1) a convex cylindrical lens with an axis along the X- direction, (2) a convex lens, (3) a convex cylindrical lens with an axis along the Y- direction, (4) a concave cylindrical lens with an axis along the Y-direction, (5) a concave lens, and (6) a concave cylindrical lens with an axis along the X-direction.

5. The sensor system of Claim 1 , wherein the light sensor is a two- dimensional photoelectric sensor.

6. The sensor system of Claim 1, wherein the light sensor is a charge-coupled device or a complementary metal-oxide-semiconductor device.

7. The sensor system of Claim 1 , wherein the single 2D grating simultaneously modulates the plural split beams with the corresponding modulations.

8. The sensor system of Claim 1 , wherein the light sensor simultaneously records the plural split beams with different modulations.

9. The sensor system of Claim 1, wherein the light intensities of the plural split beams are recorded in a single plane.

10. The sensor system of Claim 1, further comprising: one or more lenses.

11. A method for reconstruction of a wavefront of an optical beam, the method comprising: receiving (600) a coherent light beam (112) having a random, non-zero, wavefront distribution L(x,y), where x and y are Cartesian coordinates of a plane; phase modulating (602) the coherent light beam (112) with a preset phase modulation function Ø(x,y) of a single, 2-dimensional (2D) grating (110), to obtain a modulated coherent field M(x, y), wherein the modulated coherent field M(x, y) includes plural split beams (114-1), each modulated with a different modulation corresponding to the preset phase modulation function Ø(x,y); calculating (604) a coherent field D(x, y) on a plane of an optical sensor (120), wherein the coherent field D(x, y) corresponds to the modulated coherent field M(x, y); calculating (606) with a processing unit (130) a modulus constrained field D’(x, y), by imposing a modulus constraint on (1) a phase of the coherent field D(x, y) and (2) an intensity l(x, y) of the plural split beams (114-1), which is measured by the optical sensor (120); calculating (608) an error between the coherent field D(x, y) and the modulus constrained field D’(x, y); backward propagating (610) the modulus constrained field D’(x, y) to calculate a backward propagation coherent field distribution M’(x, y); calculating (612) a reversed coherent field L’(x, y) based on the backward propagation coherent field distribution M’(x, y); and outputting (618) the reversed coherent field L’(x, y) as the reconstructed wavefront of the optical beam when the error is smaller than a present threshold.

12. The method of Claim 11, wherein the plural modulations are applied by the single 2D grating in a single-shot of the incoming optical beam.

13. The method of Claim 12, wherein properties of the single 2D grating are not changing.

14. The method of Claim 11 , wherein the single 2D grating extends in a plane defined by X- and Y-directions, and the preset phase modulation function Ø(x,y) of the single 2D grating is configured to simulate (1) a convex cylindrical lens with an axis along the X-direction, (2) a convex lens, (3) a convex cylindrical lens with an axis along the Y-direction, (4) a concave cylindrical lens with an axis along the Y- direction, (5) a concave lens, and (6) a concave cylindrical lens with an axis along the X-direction.

15. The method of Claim 11, wherein the step of calculating the modulus constrained field D’(x, y) multiplies a square root of the intensity l(x, y) with an exponential of the phase of the coherent field D(x, y).

16. The method of Claim 11, wherein the step of calculating the error comprises: integrating a square of a norm of a difference between the coherent field D(x, y) and the modulus constrained field D’(x, y) over a surface of the sensor.

17. The method of Claim 11, wherein the step of backpropagating comprises: applying a Fourier transform to the modulus constrained field D’(x, y), which is multiplied by an exponential of spatial angular frequencies along the X and Y- directions, and a distance between the single 2D grating and light sensor.

18. The method of Claim 11, wherein the step of calculating the reversed coherent field L’(x, y) comprises: multiplying the backward propagation coherent field distribution M’(x, y) with an exponential of the preset phase modulation function 0(x,y).

19. The method of Claim 11, further comprising: filtering the reversed coherent field L’(x, y) with a low-filter.

20. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a computer, implement a method for reconstruction of a wavefront of an optical beam, the method comprising: receiving (600) a coherent light beam (112) having a random, non-zero, wavefront distribution L(x,y), where x and y are Cartesian coordinates of a plane; phase modulating (602) the coherent light beam (112) with a preset phase modulation function Ø(x,y) of a single, 2-dimensional (2D) grating (110), to obtain a modulated coherent field M(x, y), wherein the modulated coherent field M(x, y) includes plural split beams (114-1), each modulated with a different modulation corresponding to the preset phase modulation function Ø(x,y); calculating (604) a coherent field D(x, y) on a plane of an optical sensor (120), wherein the coherent field D(x, y) corresponds to the modulated coherent field M(x, y); calculating (606) with a processing unit (130) a modulus constrained field D’(x, y), by imposing a modulus constraint on (1) a phase of the coherent field D(x, y) and (2) an intensity l(x, y) of the plural split beams (114-1), which is measured by the optical sensor (120); calculating (608) an error between the coherent field D(x, y) and the modulus constrained field D’(x, y); backward propagating (610) the modulus constrained field D’(x, y) to calculate a backward propagation coherent field distribution M’(x, y); calculating (612) a reversed coherent field L’(x, y) based on the backward propagation coherent field distribution M’(x, y); and outputting (618) the reversed coherent field L’(x, y) as the reconstructed wavefront of the optical beam when the error is smaller than a present threshold.