INTERFEROMETER-BASED SYNTHETIC MULTI-EXPOSURE SPECKLE IMAGING (SYMESI) METHOD AND SYSTEM

Abstract

A SyntheticMulti-Exposure Speckle Imaging (syMESI) methodology necessarily utilizing an optical interferometer apparatus as part of the speckle imaging system to overcome the optical detector noise that conventionally limits the reliable and accurate determination of a speckle contrast characteristic at low exposure times. The use of such methodology enabled a quantitative determination of absolute value(s) of changes of motion at the target object (such as blood flow changes in tissue) at low photon budget of less than 40 counts of average detection intensity and/or quantitative imaging of the blood flow at the object in interoperative setting with a low-cost camera sensor.

Claims

1. A speckle imaging system comprising: an optical illumination system of the speckle imaging system including a source of light and configured to produce a light output at an output end thereof, wherein the speckle imaging system is configured to detect a motion; an optical interferometer apparatus of the speckle imaging system, the optical interferometer apparatus having a reference arm and a sample arm and optically coupled with the output end of the optical illumination system, wherein the optical interferometer apparatus is configured to not require and/or to not allow for, in operation thereof, a change of optical phase difference between a sample light propagating through the sample arm and a reference light propagating through the reference arm; an optical imaging system of the speckle imaging system, the optical imaging system containing an optical detector system that is optically cooperated with the output end; a computer system, operably connected with the optical imaging system and configured to receive an electrical signal therefrom, wherein the electrical signal represents a raw speckle image formed at the optical detector system in light output from the optical interferometer apparatus, wherein the light output includes the sample light that has interacted with a target sample in the sample arm and that contains a speckle pattern representing the target sample and the reference light; and a computer-readable tangible non-transitory medium comprising a computer-readable program code on which are stored computer-readable instructions such that, when the instructions are executed by a processor of the computer system, the instructions cause the processor at least to determine and/or display a speckle contrast characteristic of said raw speckle image.

2. A speckle imaging system according to claim 1, wherein the instructions further cause the processor: to display said speckle image as a visually perceivable spatial distribution of optical irradiance; and/or to determine and/or display a speckle visibility curve of values of the speckle contrast characteristic of said speckle image as a function of the target sample exposure times; and/or to determine and/or display a multiplicity of speckle contrast images and/or the speckle visibility curve as a map showing a spatial distribution and/or a temporal distribution of changes of said motion at the target sample.

3. A speckle imaging system according to claim 1, which satisfies at least one of the following conditions: (3a) the speckle imaging system is configured to have a dynamic range of measurement of the speckle contrast characteristic to necessarily depend on intensity of the reference light; and/or (3b) the speckle imaging system includes at least one device configured to control an intensity of the sample light and/or an intensity of the reference light; and/or (3c) wherein the instructions further cause the processor to ascertain the speckle variance of said raw speckle image while maintaining such variance to be larger than a variance of noise of the optical detector; and/or (3d) wherein the instructions further cause the processor to ascertain the speckle variance of said raw speckle image while maintaining such speckle variance to be larger than a variance of noise of the optical detector substantially regardless of a level of non-zero intensity of the first portion of said light; and/or (3e) wherein the instructions further cause the processor to quantitatively determine an absolute value of an index of motion over a portion of the scene or over the entire scene represented by a given pixel of the raw speckle image; and/or (3f) wherein the instructions further cause the processor (i) to calculate a value of speckle contrast of said raw speckle image for each identified pixel or group of pixels of the optical detector: as a first ratio of a normalized value of a standard deviation of intensities of light at pixels within a chosen area of the optical detector surrounding such identified pixel to a mean value of said intensities, or as a second ratio of a normalized value of a standard deviation of intensities of light at the identified pixel to a mean value of said intensities of light at the identified pixel calculated over multiple exposure times, and/or (ii) determine the first ratio and/or the second ratio in a temporal domain, a spatial domain, or a spatio-temporal domain.

4. A speckle imaging system according to claim 1, Wherein the speckle imaging system is configured as a multiple-synthetic exposure-time speckle imaging (syMESI) system, in which the optical illumination system does not include an apparatus that is configured to maintain a power of said light output to be substantially constant over exposure time, and wherein the instructions further cause the processor to acquire, at only one fixed first empirical exposure time, one or more raw speckle images formed in said light by the imaging system; and to spatially average a chosen raw speckle image of said one or more raw speckle images with use of multiple binning apertures that have spatial different dimensions to form respectively-corresponding modified speckle images, wherein each of said modified speckle images represents a speckle image corresponding to a respectively-corresponding second synthetic exposure time from a plurality of second synthetic exposure times, wherein each second synthetic exposure time from the plurality of second synthetic exposure times is different from one another and from the first empirical exposure time.

5. A speckle imaging system according to claim 4, wherein the instructions further cause the processor to transform each of the modified speckle images into a respectively-corresponding speckle contrast image of a plurality of speckle contrast images and/or speckle visibility curves corresponding to the same chosen image.

6. A speckle imaging system according to claim 4, wherein the instructions are configured to further cause the processor to assess, based at least on said speckle visibility curve, a quantitative value of a motion at a portion of a scene irradiated with said light output in operation of the speckle imaging system and represented by said one or more raw speckle images.

7. A speckle imaging system according to claim 4, wherein the instructions are configured to further cause the processor to generate a visually perceivable image of a portion of a scene irradiated with said light output in operation of the speckle imaging system and represented by said one or more raw speckle images, wherein said visually perceivable image displays a spatial distribution of a quantitative value of a motion at said portion of the scene via a spatial distribution of an optical parameter across said visually perceivable image.

8. A speckle imaging system according to claim 4, wherein the instructions are configured to cause the processor to acquire, at only said one fixed first empirical exposure time, a sequence of raw speckle images formed in said light by the imaging system, wherein constituent raw speckle images in said sequence are necessarily non-consecutive.

9. A speckle imaging system according to claim 8, wherein the optical imaging system is configured to acquire said necessarily non-consecutive raw speckle images with time gaps of different durations in between immediately neighboring raw speckle images.

10. A method for characterizing a scene with a speckle imaging system, the method comprising: with the use of the speckle imaging system according to claim 1: coupling light generated by a light source of the speckle imaging system into an optical interferometer apparatus of the speckle imaging system, wherein the speckle imaging system is configured to detect motion and wherein the optical interferometer apparatus is configured to not require and/or to not allow for, in operation thereof, a change of optical phase difference between a sample arm and a reference arm thereof, irradiating the scene with a first portion of said light propagating through the sample arm of the optical interferometer apparatus; spatially overlapping, at an optical detector of the optical detection system of the speckle imaging system, a second portion of said light that has propagated through the reference arm of the optical interferometer apparatus with said first portion of light that has interacted with the scene thereby forming an output light, the output light containing both the first portion of said light backscattered by the scene and the second portion of said light; and acquiring, at a given exposure time, a raw speckle image of the scene in said output light with an optical detector.

11. (canceled)

12. A method according to claim 10, devoid of changing an operational parameter of the optical interferometer apparatus during said coupling, said irradiating, said overlapping, and said acquiring, wherein the operational parameter does not include intensity of the second portion of said light.

13. A method according to claim 12, further comprising: varying a dynamic range of a speckle contrast characteristic of said raw speckle image by modifying the intensity of the second portion of said light.

14. A method according to claim 1, further comprising: determining a speckle contrast characteristic of said raw speckle image as a function of a ratio of intensity of the second portion of light to intensity of the output light.

15. (canceled)

16. A method according to claim 14, further comprising: varying a dynamic range of the speckle contrast characteristic of the raw speckle image by modifying the intensity of at least one of the first portion of said light and the second portion of said light.

17. A method according to claim 10, further comprising ascertaining a speckle variance of said raw speckle image while maintaining such speckle variance to be larger than a variance of noise of the optical detector.

18. A method according to claim 17, wherein said maintaining includes maintaining the speckle variance to be larger than the variance of noise of the optical detector substantially regardless of a level of non-zero intensity of the first portion of said light.

19. A method according to claim 12, wherein at least one of the following conditions is satisfied: (19a) the method further comprises: quantitatively determining an absolute value of an index of motion at a portion of the scene represented by a given pixel of the raw speckle image; and (19b) said index of motion is an index of blood flow when said scene is a biological tissue.

20. A method according to claim 12, comprising: (20a) calculating a value of speckle contrast of said raw image for each identified pixel of the optical detector: as a first ratio of a normalized value of a standard deviation of intensities of light at pixels within a chosen area of the optical detector surrounding such identified pixel to a mean value of said intensities, or as a second ratio of a normalized value of a standard deviation of intensities of light at the identified pixel to a mean value of said intensities of light at the identified pixel taken over multiple exposure times, and/or (20b) calculating the first ratio and/or the second ratio in a temporal domain, a spatial domain, or a spatio-temporal domain.

21. A method according to claim 12, wherein said acquiring includes acquiring, at only one fixed first empirical exposure time, one or more raw speckle images of the scene in said output light; and further comprising: for each of a plurality of binning apertures that have different spatial dimensions, modifying a chosen image of the one or more raw speckle images into a corresponding one of multiple modified speckle images by spatially averaging an irradiance distribution of said chosen image with a respectively-corresponding binning aperture of the plurality of binning apertures, thereby producing a plurality of modified speckle images each of which represents a speckle image of the scene corresponding to a second synthetic exposure time of a plurality of second synthetic exposure times, wherein all second synthetic exposure times from the plurality of second exposure times are different from one another and from the first empirical exposure time.

22. A method according to claim 21, further comprising: transforming each of the plurality of modified speckle images into a respectively-corresponding speckle contrast image of a plurality of speckle contrast images corresponding to the same chosen image.

23. A method according to claim 21, wherein: (23a) the source of light is a laser source of light; and/or (23b) for each of modified speckle image from the plurality of modified speckle images, a numerical relationship between the first empirical exposure time and the corresponding second synthetic exposure time depends on a dimension of said pre-determined binning aperture; and/or (23c) at least one of the one or more of raw speckle images, the chosen image, and at least one of the plurality of speckle contrast images is visually perceivable.

24. A method according to claim 21, wherein: (24a) said at least one or more raw speckle images includes only one raw speckle image; or (24b) two raw speckle images of said one of more raw speckle images that are acquired consecutively are acquired not immediately one after another but with an arbitrary time delay between said two images.

25. A method according to claim 21, wherein (25a) said acquiring, at only one fixed first exposure time, one or more raw speckle images, includes acquiring only one raw speckle image; and/or (25b) said modifying a chosen image of the one or more initial speckle images includes modifying of only one image of the one or more raw speckle images.

26. A method according to claim 21, wherein at least one of the following conditions is satisfied: (26a) the method further comprises: quantitatively determining an absolute value of an index of motion at a portion of the scene represented by a given pixel of the chosen image; and (26b) said index of motion is an index of blood flow when said scene is a biological tissue.

27. A method according to claim 21, wherein said acquiring includes acquiring multiple raw speckle images with time-gaps in-between at said only one fixed first empirical exposure time to form a sequence of raw speckle images in which constituent raw speckle images are necessarily non-consecutive.

28. A method according to claim 22, wherein said acquiring includes acquiring said necessarily non-consecutive raw speckle images with time gaps of different durations in between different immediately neighboring raw speckle images.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] For a more complete understanding of the disclosure, reference is made to the following detailed description and accompanying Drawings, of which:

[0024] FIGS. 1A, 1B, and 1C provide illustrations to the Laser Speckle Contrast Imaging (LSCI) methodology. Here, FIG. 1A presents a raw speckle image acquired by camera. The raw image displays random interference pattern. FIG. 1B is a processed (on the basis of the image of FIG. 1A) speckle contrast image that highlights spatial regions of high and low blood flow. FIG. 1C schematically illustrates a typical LSCI apparatus configured for two-dimensional imaging of cerebral blood flow.

[0025] FIG. 2 illustrates the results of Multi-Exposure Speckle Imaging (MESI) of rat brain. Speckle variance as a function of camera exposure duration, T, is fit to the speckle visibility equation to derive quantitative estimates of CBF at four regions of interest. Images in inset are speckle contrast images of CBF in a mouse cortex. Camera exposure duration modulates the visibility of blood vessels.

[0026] FIG. 3 schematically illustrates a typical setup for Multi-Exposure Speckle Imaging (MESI). An Acousto-Optic Modulator (AOM) is required to modulate the intensity of the laser over different exposure times. The camera and AOM are typically triggered with the data acquisition electronic circuitry (processor).

[0027] FIG. 4 schematically illustrates a speckle imaging system configured according to the idea of the invention.

[0028] FIG. 5: The use of synthetic Multi-Exposure Speckle Imaging methodology while collecting optical data with the embodiment of FIG. 4. Raw speckle images at longer exposure can be synthesized by spatially averaging images at shorter exposure. For example, speckle images at 1 ms exposure duration are synthesized by spatially averaging 4 pixels of a 0.25 ms speckle image. The averaging can be accomplished with a 22 moving window or by 22 binning. At each exposure duration, speckle contrast is computed at each image pixel in the temporal domain, by calculating the ratio of the standard deviation to mean of intensities.

[0029] FIG. 6: Characterization and comparison of results of synthetic multi-exposure speckle imaging performed with the system 300 of related art (see FIG. 3) and that configured according to the idea of the invention (see system 400 of FIG. 4). Histograms of pixel intensities for these two measurements, with intensity maps of the corresponding raw speckle images shown in insets.

[0030] FIGS. 7A, 7B illustrate the comparison between the speckle contrast maps obtained with speckle imaging performed with the use of conventional embodiment 300 of the speckle imaging system of FIG. 3 (single exposure) and those performed with the embodiment of the invention (400, of FIG. 4; synthetic multi-exposure) for flow rate 5 mm/s, Scale bar: 50 m.

[0031] FIG. 8A shows the fit of the synthetic MESI data obtained with the use of the embodiment 400 of FIG. 4 to the speckle model: Speckle variance as a function of synthetic exposure duration for different speeds. Measurements were made on samples with no static scattering layer. FIG. 8B: Performance of a MESI model with the use of the conventional embodiment 100 of FIG. 1 (curve 820) and the syMESI model with the use of the embodiment 400 of FIG. 4 (curve 810). In determining the relative changes in motion at the object. Baseline speed: 1 mm/sec. Plot of relative .sub.c to relative speed. Plot should ideally be a straight line (shown as a dashed line). The embodiment of the present invention estimates clearly enhance/extend linear range of relative .sub.c estimates as compared with the use of the conventional embodiment of FIG. 3 or conventional embodiment of FIG. 1. Error bars indicate standard error in relative correlation time estimates. Measurements were performed using microfluidic phantom with no static scattering layer

[0032] Generally, the sizes and relative scales of elements in Drawings may be set to be different from actual ones to appropriately facilitate simplicity, clarity, and understanding of the Drawings. For the same reason, not all elements present in one Drawing may necessarily be shown in another. While specific embodiments are illustrated in the figures with the understanding that the disclosure is intended to be illustrative, these specific embodiments are not intended to limit the scope of invention implementations of which are described and illustrated herein.

DETAILED DESCRIPTION OF THE INVENTION

[0033] As was alluded to above, the currently-used in related art speckle imaging technique referred to as Multi-Exposure Speckle Imaging (or MESI) and that referred to as synthetic MESI (or, syMESI) combine a more complex (as compared to that of the conventional LSCI system) instrument design with new but different mathematical models for conversion of speckle contrast into quantitative indices of blood flow.

[0034] Traditional LSCI methodology, according to which the speckle produced by backscattering of light is imaged with a single fixed exposure duration, is suitable for measuring of relative flow changes. As a result, the applicability of traditional LSCI is limited to very simplest of situations. In conventional LSCI, speckle contrast depends on the camera exposure duration, i.e., camera exposure duration modulates the visibility of blood vessels of different flow rates. Short exposure time allows to detect fast rate motion or flow, while longer exposure durations are needed to detect slow speckle intensity fluctuations associated with slow motion/flow.

[0035] Hardware-based MESI leverages this phenomenon and is experimentally suitable for recording speckle images at camera exposures of different durations (50 s to 80 ms, as shown in FIG. 2). Practically, this is accomplished by externally triggering the camera acquisition and laser, while ensuring that illumination power is kept relatively constant across the dynamic range of the measurement.

[0036] In practice, such leveraging is accomplished by externally triggering the camera acquisition and the laser light source while ensuring that power level of irradiation of the sample is kept substantially constant across the dynamic range of the measurement (see for example Parthasarathy, A. B., et al., Optics Express 16, 1975-1989; 2008)). The relationship between speckle contrast and camera exposure duration can be characterized by a speckle visibility equation which in its simplest form is given by: K(T, .sub.c)=(e.sup.2x1+2x)/2x.sup.2. Here, x=T/.sub.c, is a speckle instrumentation factor that depends on wavelength of light, detector pixel size and speckle size, T is the camera exposure duration and Tc is the speckle decorrelation timea quantitative index that is inversely proportional to blood flow. and .sub.c are estimated from a nonlinear curve fit (see FIG. 2) of the multi-exposure-time speckle data (that is, speckle data acquired by the optical detector at multiple exposure times independently) to the speckle visibility expression. This multi-exposure-time MESI methodology was shown to enable the determination of , which acts as an instrument and sample dependent calibration factor, thereby permitting imaging of baseline/absolute blood flow. In situ measurements of can also be used to quantitatively estimate blood flow index (.sub.c) from single exposure LSCI measurements. MESI was demonstrated to correct underestimation of large CBF changes and with a robust speckle visibility expression, reduced the sensitivity of speckle imagers to static tissue elements such as the skull. However, due to the bulky, complex and low temporal resolution limits the application of traditional hardware based MESI. FIG. 3 shows a typical implementation 300 of the MESI measurement apparatus used for speckle imaging, where an acousto-optic modulator (AOM) is used to control the intensity of the laser light source used for speckle imaging. (Alternatively, an array of neutral density filters can be used to control the optical power of the illumination.)

[0037] The recently developed and publicized software-based single shot synthetic MESI (syMESI) methodology (see, for example, PCT/US2022/022734) solves the problems associated with the multi-exposure-time time-averaging MESI-based implementation of the LSCI by simultaneously avoiding the need to control power of laser light irradiating the target scene (and thus allowing the user to revert to the practical use of the basic, simpler LSCI system schematically depicted in, for example, FIG. 1) and, at the same time, providing the quantitative assessment of the particle movements in the target that the conventional, single-exposure-time LSCI approach is not capable of providing. Thus, syMESI allows one to emulate the same result as those achieved with MESI but with the use of a traditional LSCI apparatus and using only one, single exposure. A typical hardware/software arrangement for syMESI was discussed in reference to FIGS. 5A, 5B, 5C of PCT/US2022/022734 and for that reason will not be addressed here in any detail. As discussed in PCT/US2022/022734, data representing raw speckle images that would beunder the conventional MESI regime recorded at longer exposure time do not have to be empirically recorded by, instead, can be synthesized or generated numerically by spatially averaging raw speckle image(s) that has/have been recorded practically at a shorter exposure. (The experimentally recorded raw speckle image is that acquired directly with/read-on by the optical detector, in a snap shot and not yet modified after such acquisition). For example, speckle images at 1 ms exposure duration can be synthesized by spatially averaging 4 pixels of a 0.25 ms speckle image. In one example, the averaging can be accomplished with a 22 moving window or by 22 binning. At each exposure durationwhether the one at which the speckle image has been acquired empirically or the one at which the speckle image has been synthesized numerically, speckle contrast is then computed with the use of a temporal, spatial, or spatio-temporal speckle image processing scheme. Synthetic speckle contrast for corresponding synthetic exposure time fit to the traditional MESI equation for estimation of flow. Both the MESI methodology and the syMESI methodology provide for quantitative imaging of an absolute value (as opposed to relative value determined with respect to some reference value) or a baseline of flow and increased the dynamic range of flow detection as compared with the conventional LSCI technique. (Notably, the term absolute value is defined herein not in a mathematical sense as a modulus of such value but as a value that represents the intrinsic magnitude of a parameter being measured without comparing it to any other, while the relative value of the parameter is determined based on comparison with a reference magnitude of a similar parameter.)

[0038] A person of skill will now immediately appreciate that both the traditional hardware-based multi-exposure speckle imaging (MESI) approach and the software-based synthetic multi-exposure (syMESI) approach utilize, for formation of raw speckle image(s), a single category, kind of lightlight scattered by the target scene or object, and both require the acquisition of speckle images/image at short exposure duration (50 s to 80 ms for MESI/(50 s for syMESI). Acquisition of images at short exposure time is, as is well recognized, a non-trivial instrumental challenge. Since speckle contrast is conventionally computed as the variance of intensities normalized to the mean value of intensities, the average intensity of the backscattered light at the camera sensor (optical detector) necessarily has to be large enough to overcome noise of the detector and to utilize the full dynamic range of the detector (for example, 127 a.u. for 8 bit and 32768 a.u. for 16 bit optical camera). This, in turn, leads to a requirement to have the target-illuminating power of light generated by the employed laser source to necessarily be high and/or expensive or, otherwise, high-sensitivity optical cameras/detectors have to be used. (The high target illuminating laser power in current context is that which produces local irradiances greater than ANSI approved limits for laser/skin exposure or other conventional limits for laser-tissue exposure.)

[0039] This limitation of the need to use the high-power laser sources reduces the significance of MESI/syMESI in clinical applications, as damage due to laser exposure simply does not allow one to work with such high target-illuminating powers, especially for sensitive tissues such intraoperative brain imaging and ophthalmology. Notably, while detection sensitivity can be, of course, increased with the use of SPAD array or EMCCD cameras, such use also increases the overall instrument cost, form factor, and complexity.

[0040] Embodiments of the invention obviate the above-described limitations and problems that are inherent in methodologies of related art by devising a speckle imaging system that employs an optical interferometer apparatus (such that light, acquired by the optical imaging portion of the overall speckle imaging system, is a composite of multiple light beams arriving to the optical imaging portion from two different origins and only one of which represents light backscattered by the target object or scene) and new speckle visibility algorithm to implement fast quantitative imaging the motion present at the object or scene while utilizing the optical image transformation according to the teachings of either conventional LSCI method, or MESI method, or syMESI method.

[0041] It is understood that implementations of the discussed idea of the invention are directed to non-intrusive imaging of and determining a motion present at various objectsbe it an inanimate object or space containing certain moving portions or elements or living objects such as a biological tissue hosting a flow of bloodall of which are within the scope of the invention. That said, the discussion of embodiments of the invention below is presented with the specific non-limiting examples of a target that is a biological tissue, for simplicity and certainty of presentation.

[0042] The idea of the invention stems from the realization that the use of the optical interferometer apparatus between the optical illumination system (that includes a source of light such as a laser source of light, in a specific case) and the optical imaging system (that includes an optical detector) under the condition that the target object or scene (that serves as the source of backscattered light for laser speckle being imaged) is located in the sample arm of such interferometerwhile the useful light (collected by the optical imaging system at the output of the interferometer apparatus) contains not only the backscattered by the target object but also light propagating through the reference arm of the interferometerboosts the weak dynamic signal that would be provided by the backscattered light only, by itself. The use of such configuration of the embodiment of the invention was shown to enable the overall speckle imaging system to substantially always operate in such a regime in which the value of speckle variance of the raw speckle image (empirically acquired at the detector in light output from the optical interferometer apparatus) was ascertained or determined with certainty and precision while maintaining this value of speckle variance to be larger than a value of variance of noise of the optical detector substantially regardless of a level of intensity of light illuminating the target object or scene placed in the sample arm of the interferometer apparatus of the speckle imaging system. By increasing the speckle variance to be over the noise level with the use of the embodiment of the invention, the signal to noise ratio of the measurement is advantageously increased. The formation of such operational regime due to the use of the optical interferometer apparatus as part of the overall speckle imaging system provides a clear operational advantage to embodiments of the invention, in stark contradistinction with operation of any speckle imaging system of related art whichas soon as the level of intensity of light illuminating the object/scene falls below a certain levelnecessarily and recognizably does not allow for any reliable, repeatable, accurate, and/precise determination of the speckle variance that is dominated by the variance of noise of the optical detector.

[0043] Furthermore, as practical implementations of the idea of the invention empirically demonstrated, the temporal resolution of the proposed speckle imaging methodology was limited only by the camera frame rates; and a high frame rate optical camera/detector was not required for the methodology to work. As a result, the proposed methodology can be used to perform quantitative video rate multi-exposure speckle imaging (which is about 10 times faster than current state of the art). The implementation of the idea of the invention provides an additional advantage in that the strength of interferogram collected in light output from the optical interferometer apparatus of the systemand hence the dynamic range of the overall measurementcan be tuned or varied at will by adjusting, for example, the intensity light in the reference arm (with the use of a neutral density filter, in one specific non-limiting case).

[0044] Notably, and in stark contradistinction with acquisition of laser speckle under different circumstances such as, for example, in the case when the optical coherence tomography (OCT) system is used, the embodiment of the invention is configured such that the optical interferometer apparatus does not require or even does not allow for a change of optical path difference (OPD that would otherwise be caused by, for example, change of phase differential) between light portions propagating through its sample and reference arms.

[0045] A representative embodiment 400 of the speckle imaging system configured according to the idea of the invention is schematically shown in FIG. 4, and, as shown, includes an optical interferometer apparatus which in this specific case is configured as a Mach-Zehnder interferometer (with understanding that in related embodiment the interferometer can be structured differently, for example according to a Michelson configuration, for example).

[0046] Light from a light source 410 (which, in one practical implementation was a single mode laser diode, LD, generating linearly polarized CW light at =638 nm and 150 mW) of the optical illumination system 414 was spatially transformed with the use of optics 418 (as showncollimated with an aspheric lens L1, Thorlabs C171TMD-B, f=6.20 mm, NA=0.30) to produce the input beam 422, which was then split into a sample beam of light 426S and a reference beam of light 426R with the use of a non-polarizing beam splitter 420. Generally, the value of the light-splitting ratio did not affect the principle of operation of the embodiment. In the illustrated case, however, the Thorlabs BS076 model of the beamsplitter 430 was used such that about 10% of the input optical power of the beam 422 was coupled as reference light 422A into the reference arm 432R of the interferometer (here, shown to contain an step-Index multimode fiber optic patch cable 424, Thorlabs M124L01, diameter 400 m, 0.50 NA), while about 90% of light power of the beam 422 was delivered in the sample arm 432S as the sample light 422S to substantially spatially uniformly illuminate the target sample 434.

[0047] The specific geometry of illuminating the sample with the sample light 426S was proven to not affect the operation of the embodiment, but in the illustrated case such illumination was provided at an angle of about 30 to 45 degrees with respect to the normal drawn with respect to the surface of the sample 434. Similarly, the specific contents of the reference arm 432R of the interferometer apparatus were proven to not affect the operation of the embodiment 400 (a related embodiment may be implemented, for example, without the use of the optical fiber cable 424. In the specific example of FIG. 4, reference light at the output of the multimode fiber 424 was collimated by a fiber collimator FC2, 424B (Thorlabs F230FC-780-780 nm, f=4.51 mm, NA=0.55). Optionally, in at least one of the sample and reference arms 432S, 432S a device configured to control intensity of light propagating through such arm can be usedas shown in the example of FIG. 4, such device was configured as a spatially-repositionable neutral density filter ND, 444.

[0048] The sample light 426S, that interacted with and was backscattered by the sample 434, was collected by a lens 438 (shown here as an optical objective, 4, NA=0.10, Olympus). Light 442S of the collected backscattered at the sample beam 426S and light 442R of the reference beam 426R at the output end of the reference arm 432R were then spatially overlapped/combined with another beam splitter 446 (herea 50/50 beam splitter from Thorlabs; CCM1-BS013) to from light 450 at the output of the optical interferometer apparatus and imaged with the optical imaging system 454 of the embodiment 400 that included, in one specific case, by a CMOS camera (Basler acA2000-165umNIR). In one implementation, the operation of the speckle imaging system was devoid of changing an operational parameter of the optical interferometer apparatus (with an optional exception of varying the intensity of reference light 442R). In one implementation, the raw speckle images were continuously recorded at a 100 Hz frame rate and 100 s exposure time.

[0049] The embodiment 400 was equipped with a computer processor (or computer system, or data processing electronic circuitry; not shown in FIG. 4) configured at least to transform images acquired at the optical detector of the optical imaging system 454 and, at least optionally, to govern the operation of the optical illumination system 414 and/or light intensity controlling device (such as device 444, when present). Such computer processor, operably connected with the optical imaging system 454 to receive electrical signal(s) from the system 454, was complemented with a computer-readable tangible non-transitory medium carrying a computer-readable program code. The code contained instructions to the processor to at least determine and/or display a speckle contrast characteristic (such as, for example, speckle variance and/or of a raw speckle image acquired with the system 454 in the light output 450 from the optical interferometer apparatus), and, optionally, to perform additional optical-image transformation steps such as, for example, determining a speckle contrast characteristic of the empirically acquired raw speckle image as a function of a ratio of intensity of the reference light 442R to intensity of the light 450 at the output of the interferometer apparatus (as will be discussed in more detail below). Instructions, provided to the processor by the code contained on the storage medium associated with the computer processor, are in one case configured to enable calculation of speckle contrast characteristic in either temporal domain, or a spatial domain, or a spatio-temporal domain, and/or with the use of a traditional MESI or syMESI algorithms. For example, in one embodiment, the instructions provided to the processor are configured to cause the processor to calculate a value of speckle contrast of the raw speckle image acquired in light 450 for each identified pixel (or group of pixels) of the optical detector of the system 454 either as a ratio of a normalized value of a standard deviation of intensities of light at pixels within a chosen area of the optical detector surrounding such identified pixel to a mean value of such intensities, or as a ratio of a normalized value of a standard deviation of intensities of light at the identified pixel to a mean value of said intensities of light at the identified pixel calculated over multiple exposure times.

[0050] A skilled artisan having the advantage of the above discussion can readily appreciate that the effect of the use of the proposed embodiment of the invention is to ensure the operation of the system in a regime in which the useful and/or informative signal (that is, that representing the backscattered by the sample light always overcomes the noise of optical detector) at low exposure durations (typically or about 100 s) and thereby to enable a quantitative determination of an absolute value (and not the relative value; absolute measurement) and/or imaging of a motion at the sample (for example, in case of a biological tissuethat of a blood flow). The use of the optical interferometer apparatus increases the measured signal (by boosting power of the reference arm), while holding noise relatively constant, thereby allowing for the signal-to-noise ratio to be higher than conventionally possible in situations with small signal and a large noise background.

[0051] For laser speckle imaging performed with the use of the embodiment 400, for example the electric field of light 450 at the output of the optical interferometer apparatus can be expressed as

[00001]$\begin{array}{cc}E\left(t\right)=E_{\mathrm{sample}}\left(t\right)+E_{\mathrm{reference}}\left(t\right)& \left(1\right)\end{array}$

[0052] Here, E.sub.sample (t) is the electric field of light 442S backscattered from sample and E.sub.reference(t) electric field of the reference light 442R. The intensity of light 450 received and detected by the optical detector of the optical imaging system 454 is:

[00002]$\begin{array}{cc}I\left(t\right)={.Math.E\left(t\right).Math.}^2& \left(2\right)\end{array}$$\begin{array}{cc}I\left(t\right)=.Math.E_{\mathrm{sample}}\left(t\right)E_{\mathrm{sample}}^{}\left(t\right).Math.+.Math.E_{\mathrm{reference}}\left(t\right)E_{\mathrm{reference}}^{}\left(t\right).Math.+2.Math.E_{\mathrm{sample}}\left(t\right)E_{\mathrm{reference}}^{}\left(t\right).Math.& \left(3\right)\end{array}$

[0053] Following Sigert relation discussed by, for example, R. Bandyopadhyay et al. (in Speckle-visibility spectroscopy: A tool to study time-varying dynamics, Rev. Sci. Instrum. 76, 1-11, 2005), the autocorrelation of the measured intensity can now be expressed as:

[00003]$\begin{array}{cc}{g}_2\left(\right)1+\left[\frac{{.Math.I_s\left(t\right).Math.}^2}{{\left(.Math.I_s\left(t\right).Math..Math.I_r\left(t\right).Math.\right)}^2}{.Math.g_1\left(\right).Math.}^2+\frac{2.Math.I_s\left(t\right).Math..Math.I_r\left(t\right).Math.}{{\left(.Math.I_s\left(t\right).Math.+.Math.I_r\left(t\right).Math.\right)}^2}{g}_1\left(\right)\right]& \left(4\right)\end{array}$$\begin{array}{cc}{g}_2\left(\right)=1+{}_1{\left|g_1\left(\right)\right|}^2+{}_2{g}_1\left(\right)& \left(5\right)\end{array}$

[0054] Here,

[00004]${}_1={\left(1-\frac{I_r\left(t\right)}{I_T\left(t\right)}\right)}^2,{}_2=2\frac{I_r\left(t\right)}{I_T\left(t\right)}\left(1-\frac{I_r\left(t\right)}{I_T\left(t\right)}\right),$

I.sub.T=I.sub.s+I.sub.r. Following the teachings of R. Bandyopadhyay et al., one can express speckle visibility as,

[00005]$\begin{array}{cc}{V}_2\left(t\right)={}_1{}_0^{T}2\left(1\frac{t}{T}\right){.Math.g_1\left(t\right).Math.}^2\frac{\mathrm{dt}}{T}+{}_2{}_0^{T}2\left(1\frac{t}{T}\right).Math.g_1\left(t\right).Math.\frac{\mathrm{dt}}{T}& \left(6\right)\end{array}$

[0055] Assuming Lorentzian distribution, g.sub.1(t)=e.sup.t/c, the speckle contrast is then expressed as:

[00006]$\begin{array}{cc}K={\left[{}_1\frac{e^{2x}1+2x}{2x^2}+2{}_2\frac{e^{x}1+x}{x^2}\right]}^{1/2}& \left(7\right)\end{array}$$\begin{array}{cc}& \left(8\right)\end{array}$$K={\left[\left(1{\left(\frac{I_r\left(t\right)}{I_T\left(t\right)}\right)}^2\right)\frac{e^{2x}1+2x}{2x^2}+4\frac{I_r\left(t\right)}{I_T\left(t\right)}\left(1\frac{I_r\left(t\right)}{I_T\left(t\right)}\right)\frac{e^{x}1+x}{x^2}\right]}^{1/2}$

[0056] Accordingly, in an embodiment of the invention, a speckle contrast characteristic of the acquired raw speckle image is determined as a function of a (time-dependent) ratio of intensity of the reference light 442R to intensity of the overall output light 450. This Eq. 8 representing a speckle visibility obtained with the use of the embodiment 400 of the system of the invention can be further fit by performing hardware based multi-exposure (MESI) or software based synthetic multi-exposure (syMESI) data processing.

[0057] Consider, for example, the implementation of the speckle imaging with the use of system 400 and the syMESI approach and algorithm discussed in reference to FIG. 4 of PCT/US2022/022734, which is reproduced here as FIG. 5. Here, at least one or a series of multiple raw speckle images 528 may be acquired by the optical detector at an only, single, fixed exposure time (empirical acquisition of raw speckle data; hereat 0.25 ms), using the embodiment 400 of the speckle imaging system (in which the system 400 necessarily does not include an apparatus that is configured to maintain a power of the light output 450 to be substantially constant over exposure time). Either one, chosen oralternativelyeach of these raw speckle images is then modified/transformed/converted to corresponding synthetic multi-exposure-time images (that is, images corresponding to multiple synthetic exposure times) by spatially averaging the camera recorded chosen image 528(j) with an appropriate spatial window or aperture (interchangeablybinning aperture). The shape of the aperture is preferably polygonal (considering the pixelated nature of raw speckle images 528) and, in a specific case, the averaging spatial aperture may have a shape of a concave polygonthat is, a polygon at least one angle of which exceeds 180 degrees. Here, as shown in the example of FIG. 5, spatially averaging the chosen raw speckle image 528(j) taken at an empirical exposure time of 0.25 ms with a 22 square window/binning aperture yields a modified image that is a synthetic exposure image 538(j). This image 538(j) is a speckle image of the scene 120 corresponding to a synthetic (not empirical) exposure time of 1 ms. Each pixel of the synthetic 1 ms image 538(j) is an average of 22=4 adjacent pixels of the camera-acquired 0.25 ms empirical exposure time image 528(j). In this manner, FIG. 5 also illustrates how a modified speckle image 548(j) corresponding to a synthetic exposure time of 2.25 ms can be formed. By repeating this process multiple timesas indicated in FIG. 5 with ellipseswith variously-shaped and/or sized binning windows for at least one (and, if needed, more than one) empirically recorded raw speckle image from the set 528, the user or the system produce a plurality of modified speckle images each of which represents a speckle image of the scene corresponding to a corresponding synthetic exposure time (of a plurality of decided upon synthetic exposure times).

[0058] Additionally and optionallyand referring again to FIG. 5in at least one specific embodiment of the invention, the information about the motion present at the imaged sample/object/scene 434 (for a non-limiting exampleinformation about blood flow in the biological tissue) may at least in one case be quantified by determining the temporal speckle contrast at each image pixel for all synthetic exposure times, i.e., by computing the value of K at each pixel according to Eq. 8. Thereby, the set(s) of modified speckle images 538(j), 548(j), and so on is transformed to a respectively-corresponding images containing information about speckle contrast. See the speckle contrast image 578(0.25) representing the spatial distribution of speckle contrast within bounds of the empirically-acquired at the exposure time of 0.25 ms image(s) 528. See also the speckle contrast image 578(1.0) representing the spatial distribution of speckle contrast within bounds of the generated, by spatial binning average, synthetic image(s) 538(j) corresponding to synthetic exposure time of 1.0 ms. See also the speckle contrast image 578(2.25) representing the spatial distribution of speckle contrast within bounds of the generated, by spatial binning average, synthetic image(s) 448(j) corresponding to synthetic exposure time of 2.25 ms. Furthermore, at each pixel of such speckle contrast image(s) one can thus assess the speckle visibility (expressed in at least one example as a plot or curve of speckle variance vs synthetic exposure time, e.g., FIG. 2) that can further be fit to either a single-scattering quantitative speckle contrast spectroscopy model (see Parthasarathy, A. B., et al., in Optics Express 16, 1975-1989; 2008)) or a diffuse-scattering quantitative speckle contrast spectroscopy model (see Valdes, C. P. et al. in Biomedical optics express 5, 2769, doi: 10.1364/BOE.5.002769 (2014).) to estimate an index of motion at a portion of the interrogated scene 434 represented by a given pixel of the chosen raw speckle image (and, in the case when the scene is a biological tissuean index of blood flow at the corresponding portion of the tissue).

[0059] Notably, the spatial averaging can be performed using a variety of approaches as befitting the applicationincluding pixel-wise binning (expressly depicted in FIG. 5) with spatial windows or apertures of various sizes and/or shapes placed substantially in the same location of the chosen raw speckle image, or with a spatial window or aperture of a fixed size and/or shaped that is repositioned across the chosen raw speckle image. The latter can retain the high spatial resolution of the images. These operations can be performed using standard image processing algorithms. Furthermore, as the skilled artisan has already appreciated from the discussion above, the spatial averaging is not restricted to a rectangularly-shaped spatial window or binning aperture. For example, with reference to FIG. 5, a 32 spatial window can be used to synthesize 0.256=1.5 ms exposure image. As applications require, windows of arbitrary (optionally-polygonal) shapes and sizes can be used.

Discussion of Experimental Results:

[0060] As was already alluded to above, one of practical advantages provided by the use of the embodiment of the speckle imaging system incorporation the optical interferometer apparatus characterized by the substantially unchangeable OPD between the sample and reference arms is the ability of such system to obtain/to boost weak dynamic signal, especially on the background of the ever-present noise of the optical detector. The use of embodiment 400 provided experimental validation of this advantage and demonstrated that imaging and quantification of absolute numerical parameter of a motion present at the target object could be carried out substantially regardless of how low the intensity of sample-illuminating light 426S was. To this end, synthetic MESI images and speckle visibility curves were computed (according to the algorithm referenced above with respect to FIG. 5) for additional multiple exposures varying from 100 s to 10 ms starting with a raw speckle image(s) acquired at a single exposure time. The raw speckle image(s) were collected from tissue simulating flow phantomwhile flowing 20% intralipid through a 200 m150 m flow channel, at flow rates 1 to 7 mm/s.

[0061] The results presented in FIG. 6 attest to the fact that the system 400 necessarily operates in a regime in which the weak dynamic signal representing light 442S is boosted to overcome the noise of the optical detector. Here, FIG. 6 compares intensity histograms of the raw speckle images acquired with the system 100 of FIG. 1 and the system 400 of FIG. 4. In case of the utilizing the embodiment 100, the average intensity of light at the optical detector of the imaging camera was 33.75 (a.u.), which is 4 times lower than the intensity required to fill the dynamic range of the 8 bit camera sensor. Also, due to the low photon counts, imaged speckle is underdeveloped. See histogram 100 and inset I.sub.100. Next, only the reference light propagating through the reference arm was introduced, embodiment 400, with an average intensity of 78.36 (a.u.). As multimode fiber was employed in the reference arm, one can control/vary/modify the intensity of the reference light to ensure that that resulting speckle pattern does not saturate the optical detector (sensor of the optical imaging system or camera). See histogram REF and inset I.sub.REF. Finally, when judiciously overlapping the backscattered by the sample light 442S with the reference light 442R and interfering those at the optical detector, the overall average intensity was increased to 113.73 (a.u.). See histogram 400 and inset I.sub.400From the inset we can clearly see dynamic speckle from the flow region boosted by the reference arm due to the heterodyne scheme compared to homodyne scheme. Further, the use of the embodiment of the invention proved the ability of the speckle imaging process to ensure quantitative imaging and determination of an absolute characteristic of the motions in presence of the noise at the optical detector.

[0062] FIGS. 7A, 7B demonstrates the reconstruction of quantitative speckle contrast images with the embodiment of the invention (FIG. 7B) and comparison of the results with those produced by the use of the traditional speckle imaging (embodiment 100; with low photon counts typical of short exposure time <1 ms). FIG. 7A illustrates that the average intensity detected by the optical detector of the embodiment 100 was low and the image was dominated by the noise of the optical detector. Application of MESI/syMESI data processing of raw images acquired with the conventional embodiment 100 may yield artificially high speckle contrast values. The resultant image of motion at the object (in this casethe image of blood flow in a biological tissue) had poor sensitivity flow in the channel present in the middle of the image, with the entire image of FIG. 7A resembling that of a static speckle pattern. The use of the embodiment 400, however, overcame this issue by boosting the low mean intensity of light backscattered by sample via interference of this backscattered light with light propagating through the reference arm, and allowed to accurately evaluate speckle contrast image at comparably short exposure time(s). It is evident from several images of FIG. 7B that speckle contrast at exposure time 100 s for example was incomparably higher than that of FIG. 7B, while at the same time enabling the accurate measurement of the absolute value of the speckle contrast despite the presence of the noise of the optical detector.

[0063] Moreover, the use of the embodiment 400 demonstrated linearity of large changes of the motion at the sample (for example, large changes in blood flow of the biological tissue) in presence of the optical detector noise in contradistinction with results obtained with the use of the conventional embodiment 100; see FIGS. 8A, 8B.

[0064] Here, the experimental setup 400 (FIG. 4) was used in conjunction with the synthetic exposure technique to perform controlled experiments on the microfluidic samples. Intralipid 20% was pumped through the sample using the syringe pump at different speeds ranging from 1 mm/sec to 7 mm/sec in 1 mm/sec increments. One hundred (100) raw speckle images were captured for each flow rate at 100 s exposure duration. Using synthetic multi-exposure algorithm average heterodyne speckle contrast, as a function of exposure time, were calculated for the flow region. The so procured synthetic multi-exposure speckle contrast data were then fit to Eq. 8, by holding and

[00007]$\frac{I_r\left(t\right)}{I_T\left(t\right)}$

constant. FIG. 8A clearly shows that the model fits the experimental data very well. The correlation time (a quantitative metric of the motion, blood flow) was estimated by having .sub.c as a fitting parameter. Next, the proof was sought of whether the .sub.c estimates obtained using the speckle imaging instrument 400 were more accurate than those obtained with traditional single exposure LSCI measures by comparing the respective estimates of the relative correlation time measures. Correlation time estimates from traditional single exposure measures was obtained using conventional methods, for example using the procedure detailed by D. A. Boas, et al. (Laser speckle contrast imaging in biomedical optics, J. Biomed. Opt. 15, 011109, 2010). Relative correlation time measures were defined as

[00008]$\frac{\mathrm{Baseline}{}_c}{{}_c},$

Correlation time estimates were obtained from the fits performed in FIG. 8A. The .sub.c estimates obtained with the system 400 were compared with those obtained with traditional single exposure utilizing the conventional system 100 of related art estimates of .sub.c at 100 s to evaluate the efficacy of predicting relative flows. Ideally, relative correlation measures would be linear with relative speed. Relative correlation times were obtained for a baseline flow of 1 mm/sec.

[0065] FIG. 8B shows that the proposed speckle model in conjunction with the use of speckle imaging system 400 and synthetic multi-exposure speckle imaging scheme achieved linearity of relative correlation measures over a large flow range (nearly 6-fold; compare data curve 810 with the linear dashed line) while easily overcoming the presence of the optical detector noise. At the same time, the use of traditional single exposure scheme of embodiment 100 (see curve 820) failed to provide any relative change of the motion at the imaged object/scene since the useful (backscattered by the object) signal was completely buried by the noise of the optical detector. Indeed, to evaluate linearity of relative change of motion (blood flow in one specific example), the average detected intensity needed to be at least 127 (a.u) for a 8 bit optical detector and 32768 (a.u) for a 16 bit optical detector. This allowed full utilization of the dynamic range of the optical imaging system and full development of the speckle. The use of embodiment 100, on the other hand, at such short exposure time (<1 ms) fell short of achieving this dynamic range in each case when and unless high laser power and sensitive detector were used.

[0066] The skilled artisan will now appreciate practical advantages provided by the use of the proposed embodiment of the speckle imaging system over comparable optical instruments of related art in imaging/measuring a motion occurring at the target object or sample or scene:

[0067] the proposed instrument requires only addition of a reference arm to the conventional speckle imaging apparatusthis can be achieved in free-space as shown in FIG. 4, or with the use of an optical fiber component, or other similar arrangement. Any low power laser source and low-cost camera (as low as 1 megapixels, low bit depths and light sensitivities) can be used.

[0068] No special expensive high-power laser or instruments are required for overcoming the optical detector noise.

[0069] In the case of utilizing single-shot imaging, the temporal resolution of the approach is limited only by the frame rate of the optical detector; a high frame-rate camera is not required for the methodology to work. As a result, the discussed embodiment can be used to perform quantitative video rate multi-exposure speckle imaging (about 10 times faster than current state of the art).

[0070] The strength of the acquired interferogram, and hence the dynamic range of the measurement, can be easily by adjusting the intensity of light in the reference arm.

[0071] Embodiments of the invention can be readily used in a wide variety of applications. For example, it can be applied in those applications that utilize laser speckle contrast imaging for blood flow imaging (including, but not limited to imaging of skin microvascular function and dysfunction, wound healing angiogenesis, diagnosis of tissue burns, skin cancer, endoscopic surgical procedures and GI tract surgery, ulcer and/or cardiovascular studies, ophthalmology, diabetes, cerebrovascular studies and especially, intraoperative surgery. It can be also advantageously utilized in quantification of speckle fluctuation dynamics in any multi-speckle detection system, including that applied for diffuse speckle contrast analysis, laser speckle rheology and speckle-based thrombosis measurements.

[0072] Contents of each of related art references and/or articles identified in this disclosure is incorporated herein by reference.

[0073] References throughout this specification to one embodiment, an embodiment, a related embodiment, or similar language mean that a particular feature, structure, or characteristic described in connection with the referred to embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases in one embodiment, in an embodiment, and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment. It is to be understood that no portion of disclosure, taken on its own and in possible connection with a figure, is intended to provide a complete description of all features of the invention.

[0074] For the purposes of this disclosure and the appended claims, the use of the terms substantially, approximately, about and similar terms in reference to a descriptor of a value, element, property or characteristic at hand is intended to emphasize that the value, element, property, or characteristic referred to, while not necessarily being exactly as stated, would nevertheless be considered, for practical purposes, as stated by a person of skill in the art. These terms, as applied to a specified characteristic or quality descriptor means mostly, mainly, considerably, by and large, essentially, to great or significant extent, largely but not necessarily wholly the same such as to reasonably denote language of approximation and describe the specified characteristic or descriptor so that its scope would be understood by a person of ordinary skill in the art. In one specific case, the terms approximately, substantially, and about, when used in reference to a numerical value, represent a range of plus or minus 20% with respect to the specified value, more preferably plus or minus 10%, even more preferably plus or minus 5%, most preferably plus or minus 2% with respect to the specified value. As a non-limiting example, two values being substantially equal to one another implies that the difference between the two values may be within the range of +/20% of the value itself, preferably within the +/10% range of the value itself, more preferably within the range of +/5% of the value itself, and even more preferably within the range of +/2% or less of the value itself.

[0075] The use of these terms in describing a chosen characteristic or concept neither implies nor provides any basis for indefiniteness and for adding a numerical limitation to the specified characteristic or descriptor. As understood by a skilled artisan, the practical deviation of the exact value or characteristic of such value, element, or property from that stated falls and may vary within a numerical range defined by an experimental measurement error that is typical when using a measurement method accepted in the art for such purposes.

[0076] The term image generally refers to an ordered representation of detector output corresponding to spatial positions. For example, a visual image may be formed, in response to a pattern of light detected by an optical detector, on a display device X such as a video screen or printer. The term quantitative is defined as that which is or may be represented by quantity.

[0077] The invention as recited in claims appended to this disclosure is intended to be assessed in light of the disclosure as a whole, including features disclosed in related art to which reference is made.

[0078] While the invention is described through the above-described exemplary embodiments, it will be understood by those of ordinary skill in the art that modifications to, and variations of, the illustrated embodiments may be made without departing from the inventive concepts disclosed herein. Disclosed aspects, or portions of these aspects, may be combined in ways not listed above. Accordingly, the invention should not be viewed as being limited to the disclosed embodiment(s).