阅读说明：本技术 用于使用静态几何偏振操纵的偏振测定的方法和系统 (Method and system for polarimetry using static geometric polarization manipulation ) 是由 W·B·斯帕克斯 于 2019-11-08 设计创作，主要内容包括：公开了用于使用偏振状态的静态几何操纵的偏振测定的系统和方法的实施方案。根据一个实施方案,一种分光偏振计包括具有几何变化快轴的延迟器。所述快轴沿着测定偏振的维度变化。所述分光偏振计具有偏振分析器和光谱光学平台。所述光谱光学平台具有：狭缝,所述狭缝在与所述延迟器的所述测定偏振的维度相同的空间维度上；准直器；分散元件,用于将从所述准直器接收的光的光谱分量沿着垂直于所述狭缝的所述空间维度的光谱维度分散；聚焦光学器件；以及二维探测器阵列。使用四分之一波延迟器可以提供完整的斯托克斯偏振测定,但是也可以使用半波延迟器。(Embodiments of systems and methods for polarimetry using static geometric manipulation of polarization states are disclosed. According to one embodiment, a partial polarization analyzer includes a retarder having a geometrically varying fast axis. The fast axis varies along the dimension of the measured polarization. The spectropolarimeter has a polarization analyzer and a spectral optics platform. The spectroscopic optical platform has: a slit in the same spatial dimension as the polarization-determining dimension of the retarder; a collimator; a dispersion element for dispersing spectral components of light received from the collimator along a spectral dimension perpendicular to the spatial dimension of the slit; a focusing optic; and a two-dimensional detector array. The use of a quarter-wave retarder may provide a complete stokes polarization determination, but a half-wave retarder may also be used.)

1. A light-splitting polarimeter, comprising:

a retarder having a geometrically varying fast axis, wherein the fast axis varies along a dimension of a measured polarization;

a polarization analyzer; and

a spectroscopic optical platform, the spectroscopic optical platform comprising:

a slit in the same spatial dimension as the polarization-determining dimension of the retarder;

a collimator;

a dispersion element for dispersing spectral components of light received from the collimator along a spectral dimension perpendicular to the spatial dimension of the slit;

a focusing optic; and

a two-dimensional detector array.

2. The spectroscopic polarimeter of claim 1 in which the retarder comprises a quarter wave retarder having a fast axis that varies continuously along a selected axis or is microscopically patterned.

3. The spectroscopic polarimeter of claim 1 in which the retarder comprises a plurality of quarter-wave plates in which the fast axis of a first strip is at a selected angle to the fast axis of a second strip adjacent to the first strip.

4. The spectroscopic polarimeter of claim 1 wherein:

the geometric change fast axis is rotated 180 ° m times and each rotation comprises n different orientations of the fast axis;

one orientation of the fast axis corresponds to k pixels of the detector array; and is

The detector array includes (x ═ m × n × k) pixels in the polarization-determining dimension.

5. The spectropolarimeter of claim 4 wherein the detector array comprises y pixels in the spectral dimension, x being independent of y.

6. The spectroscopic polarimeter of claim 4 wherein:

the width of one pixel is w; and is

The length of the delay is about y x w.

7. The spectroscopic polarimeter of claim 6 wherein:

the width w of one pixel is about 15 μm; and is

One orientation of the fast axis corresponds to 4 pixels.

8. The spectroscopic polarimeter of claim 1 in which the retarder comprises a plurality of half-wave plates in which the fast axis of a first strip is at a selected angle to the fast axis of a second strip adjacent to the first strip.

9. The spectroscopic polarimeter of claim 1 in which the retarder comprises a conical fresnel rhomb.

10. The spectroscopic polarimeter of claim 1 in which the polarization analyzer comprises a beam splitter, a wollaston prism or a savart plate.

11. A method of performing optical spectroscopy, the method comprising the steps of:

receiving electromagnetic radiation (EMR) at a retarder having a geometrically varying fast axis, wherein the fast axis varies along a dimension that determines polarization;

passing the EMR out of the retarder through a polarization analyzer; and

passing the EMR exiting the polarization analyzer through a spectroscopic optical platform having:

a slit in the same spatial dimension as the polarization-determining dimension of the retarder;

a dispersive element for dispersing spectral components of the EMR exiting the slit along a spectral dimension perpendicular to the spatial dimension of the slit; and

a two-dimensional array of detectors is provided,

wherein the two-dimensional array records a plurality of intensities of the EMR as a single frame image, the plurality of intensities representing polarization values of the EMR along a dimension of the measured polarization and a spectral dimension.

12. The method of claim 11, further comprising processing the recorded plurality of intensities using a processor to derive one or more stokes parameters using a trigonometric function mapping the plurality of intensities to the one or more stokes parameters as a function of an angle of the fast axis relative to a spatial axis in the spatial dimension.

13. The method of claim 12, wherein the one or more stokes parameters include stokes Q and U representing linear polarization parameters and do not include stokes V representing circular polarization parameters.

14. The method of claim 12, wherein the one or more stokes parameters comprise stokes Q and U representing linear polarization parameters, and stokes V representing circular polarization parameters.

Technical Field

The present disclosure relates generally to the field of polarimetry, and in particular, to methods and systems for polarimetry using static geometric polarization manipulation.

Background

Electromagnetic radiation in the form of light is characterized by a variety of characteristics including intensity, direction of propagation, frequency or wavelength spectrum, and polarization. Analysis of the intensity and spectral characteristics of light is a common diagnostic method for inferring the relevant characteristics of the source of light and the reflective and transmissive media between the source and receiver. The collection and analysis of spectral information is the fundamental method of astrophysics and has applications in many other disciplines such as material science, remote sensing, medical diagnostics, defense, biophysics, microscopy and fundamental physics. Many astronomical spectrometers use telescopes to focus light from an astronomical source onto a slit. The light from the slit is passed to a collimator that turns the diverging beam into parallel light and then to a disperser (typically a reflective grating) to create a spectrum and then to a camera that focuses the spectrum onto a sensor such as a Charge Coupled Device (CCD). The horizontal axis of the spectral image no longer corresponds to the spatial direction in the sky, but now represents the wavelength. If the slit is at the focal plane, the vertical axis of the image still corresponds to the spatial position of the incident light source. The result is a two-dimensional, spatially resolved spectrometer image that includes bands of varying intensity (bands) that run across the image in the spectral direction and that illustrates intensity as a function of wavelength. The image contains a plurality of spectra, each spectrum corresponding to a different location in the slit, or more precisely, a different portion of the source along the slit.

Disclosure of Invention

Embodiments of systems and methods for polarimetry using static geometric manipulation of polarization states are disclosed. According to one embodiment, a partial polarization analyzer includes a retarder (detarder) having a geometrically varying fast axis. The fast axis varies along the dimension of the measured polarization. The spectroscopic polarimeter has a polarization analyzer (polarization analyzer) and a spectroscopic optical platform. The spectroscopic optical platform having a slit in the same spatial dimension as the polarization-determining dimension of the retarder; a collimator; a dispersion element for dispersing spectral components of light received from the collimator along a spectral dimension perpendicular to the spatial dimension of the slit; a focusing optic; and a two-dimensional detector array.

The above and other preferred features, including various novel details of implementation and combination of elements, will now be more particularly described with reference to the accompanying drawings and pointed out in the claims. It is to be understood that the specific methods and apparatus are shown by way of illustration and not limitation. As will be understood by those skilled in the art, the principles and features explained herein may be employed in numerous embodiments.

Drawings

Other objects, features and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments and certain modifications thereof, when considered in conjunction with the accompanying drawings, in which:

FIG. 1 depicts polarization measurements obtained using one embodiment of a spectroscopic polarimeter for different light sources;

FIG. 2 depicts polarization measurements obtained after pre-processing the raw image using the same embodiment of a spectroscopic polarimeter for the different light sources used to obtain the measurements shown in FIG. 1;

FIG. 3 depicts polarization measurements obtained using one embodiment of a spectropolarimeter for left and right circularly polarized light;

FIG. 4 shows a comparison of polarization spectra of circularly polarized light with polarization measurements obtained using one embodiment of a spectroscopic polarimeter;

FIG. 5 depicts polarization measurements obtained using one embodiment of a spectroscopic polarimeter for light transmitted through and polarized by maple leaves;

FIG. 6 schematically depicts a geometric polarization mask according to one embodiment;

FIG. 7 schematically depicts components of a spectropolarimeter and its arrangement according to one embodiment; and

FIG. 8 schematically depicts components of a spectropolarimeter and its arrangement according to another embodiment.

While the disclosure is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and will herein be described in detail. The disclosure is to be understood as not being limited to the particular forms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the disclosure.

Detailed Description

Embodiments of systems and methods for polarimetry using static geometric manipulation of polarization states are disclosed. According to one embodiment, a partial polarization polarizer includes a quarter-wave retarder having a geometrically varying fast axis. The fast axis changes direction along one dimension of the measured polarization. The spectropolarimeter has a polarization analyzer and a spectral optics platform. The spectral optical platform has a slit in a spatial dimension and produces a spectrometer along a spectral dimension orthogonal to the spatial dimension. The retarders are positioned such that the dimension of the measured polarization is the same as the spatial dimension, so as to present different states of the polarization retarders and the analyzer during generation of the spectrometer. The spectroscopic optical platform may further comprise: a collimator; and a dispersive element for dispersing the spectral components of the light received from the collimator along a spectral dimension perpendicular to the spatial dimension of the slit (which is also the polarization-determining dimension); a focusing optic; and a two-dimensional detector array.

Polarization is a property of a light wave that describes the orientation of the oscillation of the light wave. "optical spectroscopy" is a measurement of the polarization of light that has been dispersed into a continuous or line spectrum as a function of wavelength. Optical spectroscopy provides a multifunctional diagnostic tool kit. For example, in astrophysics, polarimetry can be used to infer the characteristics of a physical dust when it scatters light from an adjacent star. When scattered by dust, the starlight becomes polarized in a manner that depends on the size, porosity and composition of the dust particles. These properties can be measured using polarimetric information of the scattered light. Therefore, scientific research based on optical spectroscopy techniques, especially in the field of astronomy, where optical spectroscopy is providing important clues about planets, stars and universe origin, is undergoing a rapid stage of development. As with spectroscopy, polarimetry is commonly used in medicine, remote sensing and physical science in a wide variety of applications.

The polarization properties of light can be described by the stokes vector (I, Q, U, V) where I is the total intensity, Q and U produce linear polarization in each of two planes at 45 degrees to each other perpendicular to the direction of wave propagation and V is circular polarization (circular polarization). The normalized Stokes polarization parameters (Q, u, and V) represent the fractional polarization states (Q/I, U/I and V/I, respectively). Traditionally, polarization measurements are performed sequentially with polarizing filters in different orientations, with rotatable wave plates, or with complex fragile fast modulation components such as ferroelectric liquid crystals and resonant crystal photoelastic modulators (PEM) to achieve high accuracy. However, sequential measurements require moving parts, and modulating components often results in inherent monochromatic performance and component fragility, all of which introduce mechanical complexity, the possibility of error, and often reduce the utility of polarimeters. In fact, polarimeters employing such schemes have limited performance because of the need for sequential measurements, or are too impractical for reliable deployment in a space-based astronomical stage.

In various embodiments, the system can perform stokes polarization measurements without any moving parts. These embodiments are compact and robust, and can encode complete polarization information on a single data frame based on static geometric polarization manipulation. In particular, by mapping the rotation of the fast axis of the retarder with the fast axis of its orientation changed to a position along a spatial axis, polarimeters according to embodiments are configured to acquire their data on a single data frame without any moving parts.

Some embodiments employ a quarter-wave retarder in conjunction with a polarization analyzer whose fast axis varies in direction with position along one axis of the 2D data frame. A complete set of stokes parameters is encoded with maximum sensitivity to circularly polarized stokes parameters V. The linear and circular polarization terms are encoded using different spatial frequencies, which minimizes or eliminates crosstalk. Other rotating component polarimeters may be adapted to similar geometric configurations. For example, if a half-wave retarder is used instead of a quarter-wave, the linear stokes parameters are encoded. The embodiments described herein are achromatic in the sense that any particular fast axis direction is substantially constant with respect to wavelength, and as such, the polarization modulation spatial frequency does not vary with wavelength. Since the polarization measurement information is acquired in a single observation, transient or moving targets are accessible and the achromatization is suitable for the design for optical spectroscopy or for measuring polarization imaging.

The following disclosure provides many different embodiments or examples for implementing different features of the subject matter. Specific embodiments of components and arrangements are described below to simplify the present disclosure. Of course, these are merely examples and are not intended to be limiting. In addition, the present disclosure may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed.

Advantages of a polarimeter that provides intensity modulation on a single data frame in this manner include: small size; a compact, robust design; the operation is simple and convenient because moving parts are not needed; a high dynamic range; and achromatism. Polarimetry obtained on a single data frame can be applied to a normal set of targets for measuring polarization, and in addition moving, time-varying or transient sources can be analyzed.

Retarders or waveplates alter the polarization state of light by using the difference in refractive index with direction. In a conventional wave plate, the optical axis of the wave plate is parallel to two parallel surfaces of the wave plate, wherein light is incident on one of said surfaces in the normal direction. The ordinary axis (organization axis) of the wave plate is perpendicular to the optical axis, and the extraordinary axis (organization axis) of the wave plate is parallel to the optical axis. Refractive indices along ordinary and extraordinary axes-n respectively_oAnd n_e-is different. Thus, the corresponding velocities of the polarization components along the ordinary and extraordinary axes-v, respectively_o＝c/n_oAnd v_e＝c/n_e-is different. Wherein n is_o＞n_eBecause v is_e＞v_oSo the extraordinary axis is the fast axis and the ordinary axis is the slow axis, and where n is_e＞n_oWhen, because v_o＞v_eThe ordinary axis is the fast axis and the extraordinary axis is the slow axis. The fast axis direction can be made position-dependent using liquid crystal technology to apply patterns on a small spatial scale or by assembling waveplates from individual parts each having a different fast axis directionA patterned retarder.

Retarders or geometric masks with spatially varying fast axes can be fabricated using various methods, including those employed in vector vortex coronagraphy (vector vortex coronagraphy). Using micro-scale formulations of polarizing elements using Ultraviolet (UV) cured polymers and liquid crystal technology, masks can be created in which the orientation of the fast axis varies continuously with position along one axis of the mask/retarder for all intents and purposes. As used herein, "continuously" means that the angle of the retarder fast axis varies smoothly with position, and successive orientations are close enough together to appear continuous.

In the case of a vector vortex coronagraph, the waveplates forming the retarder have a constant retardation (retardance), but the fast axis direction varies with azimuth around a center or singularity. The "charge" m on the mask refers to the number of 180 degree rotations of the fast axis when the azimuth angle is changed by 2 π radians. Using similar manufacturing methods, smooth changes in fast axis position angles along the cartesian axes x or y are expected (e.g., less than 10 °,5 °, etc.).

Referring to FIG. 6, one embodiment of a spectroscopic polarimeter includes a retarder (e.g., retarder 10) constructed of quarter-wave plates made of polymer at a suitable set of fast axis angles that are reoriented so that the strips are parallel. The device can function as a complete stokes polarimeter and can produce high quality results. In one embodiment, retarder 10 includes eight strips having a width slightly less than 1 millimeter (e.g., within a tolerance of 20%, 10%, 5%, 2%, 1%, 0.5%, 0.1% relative to a nominal width such as 1 mm) and a length of a few centimeters (e.g., 1cm, 1.5cm, 2cm, 5cm, etc.) cut from the quarter-wave retarder film at positional angles from horizontal to 157.5 degrees corresponding to 22.5 degree increments. The strips are glued adjacent to each other to a rectangular linear sheet polarizer, resulting in a fast axis direction that varies with position across the strips. Although the retarder assembly 10 is divided and repeated to increase the number of strips presented to the spectrometer, only a single cycle of eight strips is used in the analysis.

It should be understood that although the retarder assembly 10 includes eight stripes, retarders having fewer (e.g., 4, 6) stripes and more (e.g., 10, 12, 16, etc.) stripes may be used in different embodiments. It is also understood that the angular increment or angle of one strip relative to an adjacent strip may be less than or greater than 22.5 degrees, depending on the number of strips used. For example, if 12 strips are used, the change in angle may be 15 degrees. The retarder assembly 10 may be mounted on a microscope slide, framed by the same material for support, and protected with a front cover glass microscope slide. The long slit may be fixed behind the mounted slide.

In one embodiment, a spectroscopic polarimeter includes a retarder having a fast axis and an entrance aperture in multiple directions, a Richardson transmission grating, and a QSI CCD camera. Test exposures were obtained using white light, left and right circularly polarized light from 3D cinema glasses, cholesteric liquid crystal filters, linearly polarized light, and maple leaves. 532nm green laser light and 650nm red laser light were used to approximate the calibration wavelength. FIG. 1 shows raw data exposed from a device. The black gaps correspond to the junctions (joins) between adjacent bars. Fig. 2 depicts the data of fig. 1 after pre-processing to remove artifacts and gaps associated with the junction, so it is similar to data that would emerge from a mask whose orientation varies continuously from the fast axis, showing spectra extracted from the raw data and proportional to the average white light spectrum. As a device to measure circular polarization, note that (a) the modulation amplitude for V is twice that of Q or U for the same degree of polarization, and (b) since V is modulated to a linear term at half the spatial frequency, in principle, there is no crosstalk between the two.

Referring again to fig. 1, the following embodiment is depicted showing four original data frames:

the upper left frame (110) shows white light, with wavelengths decreasing from left to right;

the upper right frame (120) shows linearly polarized light, where the gaps between the bars are where the bars abut each other;

the lower left frame (130) shows left circularly polarized light; and

the bottom right frame (140) shows right circularly polarized light.

FIG. 2 depicts a processed spectral bin 200 of raw data from FIG. 1, the spectral bin 200 including eight flat-field extracted spectra with quarter-wave fast axis position angles varying by about 22.5 between spectra. The wavelength ranges from about 590nm to 670 nm. The top left frame (210) corresponds to a single white light frame, the top right frame (220) corresponds to linearly polarized light, the bottom left frame (230) corresponds to left circularly polarized light, and the bottom right frame (240) corresponds to right circularly polarized light. We see that linearly polarized light has twice the spatial frequency of circularly polarized light, and the expected sign change without phase shift between left and right circularly polarized light.

Fig. 3 shows polarization measurements of left and right circularly polarized light obtained by directing the input beam through the left and right lenses of inexpensive 3D cinema glasses. The glasses also exhibit a large number of desired linear polarizations. In particular, fig. 3 shows the derivative polarizations of left and right circularly polarized light obtained using white light illuminated through a pair of appropriately oriented 3D cinema glasses. The solid curves 302, 304 represent the circular polarization of the left and right circularly polarized light, respectively. Dashed curves 306, 308 represent the linear polarization of the left and right circularly polarized light, respectively. Left circularly polarized light (curves 302, 306) is associated with the left lens and right circularly polarized light (curves 304, 308) is associated with the right lens.

Referring to fig. 4, curve 402 shows the polarization derived from the stokes parameters of electromagnetic radiation transmitted through a cholesteric liquid wafer-shaped polarizing filter. Curve 404 in inset 406 shows the polarization of the filter as specified by the manufacturer of the filter. Note that the ripple 408 observed in the derived data 402 is also present in the manufacturer provided curve 404 at 410.

Referring to fig. 5, curve 502 shows the circular polarization spectrum of light transmitted through maple leaves. Curve 502 shows the characteristic structure associated with the chlorophyll absorption band at approximately 670nm (e.g., between 650nm and 700 nm). For comparison, curve 504 shows an analysis of unpolarized white light. The Root Mean Square (RMS) of the latter is 0.19% in stokes V. The input beam is transmitted through the maple leaf and a significant level of circular polarization is found to have a shape similar to previous measurements of the leaf. As can be seen in fig. 5, the noise level of a single white light frame in stokes V is less than 0.2%, thus indicating an unexpectedly high quality performance by the implementation of the spectropolarimeter used.

As described below, one embodiment of a spectroscopic polarimeter can be constructed using geometric polarization masking techniques. A typical detector pixel size is 15 μm; a band at a particular fast axis angle or orientation may cover, for example, 4 detector pixels. Thus, a strip of about 60 μm along the length of the slit may provide a 1:1 mapping between the slit and the detector, and may be fabricated using currently available fabrication techniques. To span one cycle using eight angles, repeated twice, i.e. with a charge m of 2, the length of the wafer will be close to 1mm (exactly 0.96mm) since 2 × 8 × 4 × 15 μm is 0.96 mm. Likewise, the extent or length of the device along the slit will be 2mm for m-4. In the spatial direction, the equivalent range on the detector is 64 pixels or 128 pixels, respectively.

Typically, if each fast axis orientation covers k detector pixels, the number of different orientations/angles of the fast axis in one 180 ° rotation is n, and if the number of 180 ° rotations is m, the number of pixels in the detector array in the spatial dimension or polarization-determining dimension (X) is m × n × k. If the width of each pixel is w, the length of the retarder in the spatial dimension is approximately equal to m × n × k × w. The spatial wavelength and the desired coverage in the spatial dimension (X) are free parameters-completely independent of the spectral configuration in the orthogonal direction (Y), as well as the selection of fast axis angles and their sampling-i.e. the difference between the angles or orientations of adjacent fast axes. For example, if a very large number of photons need to be collected over a single frame to provide accurate polarization measurements, it may be appropriate to propagate the light more broadly. This can also average out detector artifacts and pixel response variations. Furthermore, in view of the possible compactness of such a device, additional components, such as a rotating half-wave plate or a gap without polarizing elements at all, etc., may be provided along the same slit.

In some embodiments, static encoding of the polarization output may be obtained without the use of a rotating fast axis quarter wave retarder. For example, a conical Fresnel rhomb (Fresnel rhomb) may be a substitute for a quarter-wave retarder with a spatially varying fast axis direction, resulting in similar polarization modulation on the output circular rather than straight spatial axis, and may be used with a fixed position angle analyzer. At the (wider) base of the rhombus, proceeding around the output circumference of the rhombus, the fast axis direction remains radial and therefore rotates with the azimuth position. At the same time, it is assumed that the orientation of the analyzer remains fixed, so the net combination produces a similar retarder/analyzer combination as discussed above, and a continuous modulation that maps onto a circle rather than a straight line. The modulated output can be fed to the spectrometer using an optical fiber or lens.

In some embodiments, the polarization analyzer is implemented using crystal optics such as a Wollaston prism or a Savart plate. The use of these components may be more effective when the electromagnetic radiation includes Ultraviolet (UV) or Infrared (IR) radiation. The use of a beam splitter to produce a dual beam version of the polarimeter can recover a factor of v 2 in the signal-to-noise ratio. The geometric polarization mask can also be fabricated using a sheet-like polymer assembly, in which the fast axis orientation in each bar is adjusted by a machine tool (machine tool). Thus, using these inexpensive materials, it is feasible to assemble at very low cost a very large number of spectroscopic polarimeter devices that can provide complete stokes polarimetry or linear polarimetry.

The geometric polarization mask may mimic the rotation of the retarder. Liquid crystal technology can produce optically cured variable analyzer position angles, equivalent to rotations. Considering the two together, multiple combinations may be configured to produce data on a single frame of data without moving parts. These combinations include: a rotation analyzer; the rotating analyzer is fixed with the fixed analyzer; a rotating retarder ruggedized analyzer; a rotational retarder and a rotational analyzer; rotating retarders and analyzers to reinforce fixed analyzers, etc. In some embodiments, a static half-wave plate with varying fast axis position angles may be used to eliminate linear polarization in measurements of circular polarization of a target, where a spectroscopic polarimeter will provide not all but some of the stokes parameters.

The techniques described above can be applied to imaging polarimetry, taking into account the achromatization of fringes that do not depend on retardation but on the fast axis direction. In general, polarization modulation is not "deselected" due to retardation dependence on wavelength. Using appropriate optics to spread the light perpendicular to the input spatial slit, a push-broom imager (push broom imager) can be constructed using spatial dimensions that are alternative to spectral dimensions. In some embodiments, a pixelated imaging device with a resolution of 2x 2-4 or 3x 3-9 pixels in the focal plane encodes a full stokes or linear polarimetry in the middle or at the detector, and may be used with broadband or narrowband filters. In particular, using geometric polarization masking techniques, some embodiments feature a pixelated wafer, such as a pixelated quarter-wave retarder fixed to a linear polarizer. Four or nine pixel blocks may encode all four stokes parameters with different quarter wave fast axis position angles as shown in fig. 6. Specifically, the retarder 600 shown in fig. 6 includes a number of retarder macropixels 602 arranged in a grid or array. Each macro-pixel 602 includes a set of nine individually oriented retarders 604.

Classical and optical spectroscopy for polarimetry are reconfigured to acquire data using a single two-dimensional data frame by mapping the time dimension of a rotating fast axis retarder-based polarimeter into the spatial dimension using geometric polarization masking techniques, or simply by assembling such devices macroscopically. Advantages of this technique include compact design, robustness, increased fidelity to time-variable or moving targets, and reduced complexity and/or cost of design and/or manufacture, as the device does not include any moving parts. Embodiments featuring a varying fast-axis quarter-wave plate retarder may be effective in measuring the circular polarization of a target, which may have application in remote life sensing because it uses two different carrier frequencies for circular polarization and linear polarization.

Referring to FIG. 7, a spectroscopic polarimeter 700 according to one embodiment includes a slit 2, a collimator 4, a dispersive element 6, a focusing wafer 8, and a two-dimensional detector array 9. Further, the spectroscopic polarimeter includes a retarder 10. Retarder 10 has a geometry-changing fast axis and a polarization analyzer, as described above. Light (typically electromagnetic radiation) collected by the telescope, for example from an astronomical point source or a point within an extended source, is imaged onto the long slit and enters the slit 2 of the spectropolarimeter. The wafer may be used to spread light along the slit. The light coming out of the slit is collimated at a collimator 4, which collimator 4 may be a lens or a mirror element. In fig. 6, the spatial dimension (and corresponding spatial axis X) of the slit 2 is perpendicular to the plane of the page (in the upper half of the illustration), and the spectral dimension (and corresponding spectral axis Y) is perpendicular to the propagation direction/propagation axis Z in the plane of the page.

Then, the light is dispersed into its component wavelengths at the dispersing element 6. The dispersive element 6 may be a conventional prism or a diffraction grating as is more common in modern spectrometers. The focusing optics 8 may comprise one or more lenses for focusing the component dispersed light onto the two-dimensional surface of the detector array 9. The detector array 9 may be a conventional celestial photometer two-dimensional CCD or CMOS rectangular photodetector array having a plurality of light sensitive pixels arranged in a rectangular array of rows (parallel to the spatial axis X defined by the straight slits 2) and columns (parallel to the spectral axis Y). The slit 2 is imaged by spectrometer optics 4, 6, 8 onto a detector array 9. The spectral axis Y of the component dispersed light is oriented generally perpendicular to the slit 2.

The detector array 9 detects and records the intensity of the incident light at each wavelength. Thus, the detector array 9 acts as an electron photon collector. A typical CCD camera for astronomical applications comprises a layer of semiconductor materialA two-dimensional array of photon detectors positioned at the focal plane of the telescope to collect the image. Each individual detector in the array 9 is referred to as a pixel and utilizes the photoelectric effect in which electrons are released and stored in the detector in proportion to the number of photons from the source that strike the detector surface of the pixel. Thus, each pixel in the detector array 9 functions as an electron trap that accumulates released electrons in proportion to the intensity of light falling thereon, i.e., the number of incident photons. The number of electrons that can accumulate in each pixel is called the well depth and a typical astronomical CCD has about 10⁵Well depth of individual electrons.

Since a large number of photons (e.g., about 10) need to be collected for accurate polarimetry⁸One) to measure 10^-4May be required to read out (i.e. empty) the collected electrons from the well multiple times during a single observation. The solution to this problem is to spread the light from the slits 2 out onto more than one well or pixel on the surface of the detector 9, so that the incident photons are distributed over and collected by a larger number of wells, which together have a larger electron capacity. Thus, multiple wells require less readout and therefore less time to accumulate a detectably large number of electrons.

If the light entering the slit 2 is polarized and if the direction angle phi of the fast axis of the quarter wave retarder varies with the position x along the slit 2 of the spectrometer followed by the polarizing filter, the intensity of the light detected at a given wavelength along the spatial axis of the detector array 9 is modulated according to one or more of the polarization parameters, with the spatial coordinate x on the detector mapped onto the fast axis direction angle phi at any point along the slit of the spectrometer.

In view of the optical platform described above, light intensity modulation is induced along the slit 2-given by 0.5 × Q cos (4 Φ), where Φ is the angle between the retarder fast axis and the polarizing filter transmission axis or x in the detector 9 coordinates, and the angle Φ is assumed to be known by calculations refined by calibration. Referring to fig. 2, it is observed that the intensity of light of a given frequency varies along the spatial axis x according to a triangular waveform. The linearly polarized stokes component U at 45 degrees to the slit 2 is given by 0.5 × ussin (4 Φ) in the same way as the Q component. However, the circular polarization component V of the incident light produces an intensity modulation equal to V sin (2 φ). Q, U and the intensity modulations of the V components are combined on the two-dimensional detector array 9 to form a single imaged waveform with constituent elements for light of a given wavelength.

Referring to FIG. 8, according to a spectroscopic polarimeter 800 according to one embodiment, a telescope 802 receives light (typically EMR) and captures an image from a source, which then passes through a slit 804. Light exiting the slit 804 passes through a single retarder/polarization analysis optic 806. Light emerging therefrom is received at a microlens array 808, the microlens array 808 serving to segment the image captured by the telescope 802. The detector/camera 812 is used to obtain multiple images of the rectangular entrance slit using its polarization analysis optics 806. Thus, the polarization of the light passing through each microlens individually can be obtained. A disperser 810 may be used before the detector 812 so that spectral polarization measurements may be performed.

Mueller (Muller) matrix analysis can be used to derive an expression for intensity modulation that now encodes I, Q, U and the V-polarization component as linear coefficients of a trigonometric function. Thus, using the array of measured intensities, the corresponding complete stokes parameter sets I, Q, U and V can be calculated using linear least squares analysis. This is an advantage over various other techniques that encode polarization information along the spectral dimension (perpendicular to the dispersion direction of the slits), because encoding in the spectral dimension requires the use of fourier analysis, which can be quite unstable for spectral structures unwrapped from polarization modulation in the presence of incomplete waveforms.

The above example embodiments have been described herein above to illustrate various embodiments for implementing a single-shot (single-shot) static, geometry-based polarimeter. Various modifications and departures from the disclosed example embodiments will occur to those skilled in the art. The subject matter which is intended to be within the scope of this disclosure is set forth in the appended claims.

The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the invention. However, it will be apparent to one skilled in the art that the specific details are not required in order to practice the invention. Thus, the foregoing descriptions of specific embodiments of the present invention are presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed; many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the claims and their equivalents be filed later define the scope of the invention.