Measurement-diverse imaging and wavefront sensing with amplitude and phase estimation
View Patent ↗A system and method for imaging one or more objects in the presence of unknown phase and amplitude aberrations is described. Multiple images are collected so as to have measurement diversity and processed using a model-based approach to estimate the aberrations. An incoherent imaging model may be constructed to estimate the dependence of the imagery upon the object and the optical system, including the aberrations. A probability density function may then be calculated using the estimated model. Next, a maximum-likelihood estimate may be calculated and optimized, thus yielding a close approximation of the phase and amplitude aberrations. The estimates may then be used to estimate an image of the object or correct the system for future imaging.
1. A method for imaging an object, the method comprising the steps of:
acquiring at least a first image and a second image of the object, the images being measurement-diverse;
estimating parameters to represent the object and phase and amplitude aberrations impacting the acquired images;
calculating a measure of likelihood that the estimated parameters correspond to the object and the phase and amplitude aberrations in the acquired images; and
repeating said steps of estimating and calculating until the measure of likelihood is substantially maximized, wherein the estimated parameters are adjusted prior to each repetition and whereby said steps of estimating, calculating and repeating create an estimated image of the object.
2. The method of claim 1 , wherein said step of estimating parameters to represent phase and amplitude aberrations includes constraining the amplitude or the object to be non-negative.
3. The method of claim 1 , wherein the images are phase-diverse.
4. The method of claim 1 , wherein the images are wavelength-diverse.
5. The method of claim 1 , wherein the images are amplitude-diverse.
6. The method of claim 1 , wherein said step of acquiring includes acquiring the first image of the object and the second image of the object using the same detector, the second image of the object being acquired while the image is perturbed by a known amount of perturbation.
7. The method of claim 6 , wherein the image is perturbed in a predefined manner by the actuation of an optical element.
8. The method of claim 6 , wherein the image is perturbed in a predefined manner by inserting a phase plate in front of the detector.
9. The method of claim 6 , wherein the image is perturbed in a predefined manner by inserting a colored filter in front of the detector.
10. The method of claim 1 , wherein said step of acquiring includes acquiring the first image of the object using a first detector and acquiring the second image of the object using a second detector, the second image of the object being acquired while the image is perturbed by a known amount of perturbation.
11. The method of claim 10 , wherein the first detector is positioned to collect the first image at a nominal in-focus or defocused position and the second detector is positioned for collecting the second image with a known amount of defocus relative to the first image.
12. The method of claim 10 , wherein the image is perturbed by a phase plate.
13. The method of claim 10 , wherein the image is perturbed by a colored filter.
14. The method of claim 1 , wherein the images of the object are acquired using incoherent light.
15. The method of claim 1 , wherein the images of the object are acquired passively.
16. The method of claim 1 , wherein the phase and amplitude aberrations are time-varying atmospheric aberrations.
17. The method of claim 1 , wherein the phase and amplitude aberrations are aberrations resulting from the system used to acquire the images.
18. The method of claim 1 , wherein the estimated image of the object is displayed.
19. The method of claim 1 , wherein the estimated image of the object is stored in a memory device.
20. The method of claim 1 , further comprising outputting parameters corresponding to the phase and amplitude aberrations of the substantially maximized measure of likelihood and using the output parameters for the correction of an optical system.
21. The method of claim 1 , wherein the step of acquiring includes acquiring images from an object illuminated by a laser having a short-coherence length.
22. A system for imaging an object, the system comprising:
a processor;
at least one JO interface electrically coupled to said processor;
at least one detector electrically coupled to said processor via the JO interface, the detector configured to acquire at least a first image and a second image of the object, the images being measurement-diverse; and
a memory device electrically coupled to said processor, said memory device including processor-readable code configured to instruct the processor to:
estimate parameters to represent the object and phase and amplitude aberrations impacting the acquired images;
calculate a measure of likelihood that the estimated parameters correspond to the object and the phase and amplitude aberrations impacting the acquired images; and
repeat the steps of estimation and calculation until the measure of likelihood is substantially maximized, wherein the estimated parameters are adjusted prior to each repetition and whereby the estimation, calculation and repetition create an estimated image of the object.
23. The system of claim 22 , further comprising at least one analog-to-digital converter for digitizing the acquired images prior to being acquired by said processor.
24. The system of claim 22 , wherein the first image of the object and the second image of the object are acquired using a single detector, the second image of the object being acquired while the image is perturbed.
25. The system of claim 24 , wherein the image is perturbed by inserting a phase plate in front of the detector.
26. The method of claim 24 , wherein the image is perturbed in a predefined manner by the actuation of an optical element.
27. The system of claim 24 , wherein the image is perturbed by inserting a colored filter in front of the detector.
28. The system of claim 22 , wherein the first image of the object is acquired using a first detector and the second image of the object is acquired using a second detector, the second image of the object being acquired while the image is perturbed.
29. The system of claim 28 , wherein the first detector is positioned to collect the first image at a nominal in-focus or defocused position and the second detector is positioned for collecting the second image with a known amount of defocus relative to the first image.
30. The system of claim 28 , further including a phase plate positioned in front of the second detector for perturbing the image.
31. The system of claim 28 , further including a colored filter positioned in front of the second detector for perturbing the image.
32. The system of claim 22 , wherein the at least one detector is one of a CCD detector, a CMOS device, a videcon, a scanning sensor, a microbolomoter and film.
33. The system of claim 22 , further comprising a display for displaying the estimated image of the object, the display being coupled to said processor via said at least one JO interface.
34. The system of claim 22 , wherein the estimated image of the object is stored in said memory for future use.
35. The system of claim 22 , wherein said at least one detector is a part of a telescope.
36. The system of claim 22 , wherein said at least one detector is a part of a microscope.
37. The system of claim 22 , wherein the estimated image of the object is used for calibration of an imaging system.
38. The system of claim 22 , wherein the system estimates the pupil of an imaging system.
39. A method for imaging an object, the method comprising the steps of:
illuminating the object with a light source having a short coherence length such that the object appears to be incoherently illuminated;
acquiring image data for the object; and
processing the acquired image data to obtain an estimate of phase and amplitude aberrations present in the acquired image data and create an estimated image of the object; wherein the image data acquired is measurement-diverse.
40. The method of claim 39 , wherein the measurement-diversity is phase diversity.
41. The method of claim 39 , wherein the measurement-diversity is wavelength diversity.
42. The method of claim 39 , wherein the measurement-diversity is amplitude diversity.
43. The method of claim 1 , wherein the estimating comprises a Coherent Transfer Function for the k th diversity channel given by:
H k ( u ; α, β)= C ( u ; β) e i[φ(u;α)+θ k (u)]
where:
k is the index of the phase diversity channel;
u is a two-dimensional spatial-frequency coordinate vector;
α is a phase-aberration parameter vector;
β is an Coherent Transfer Function amplitude-aberration parameter vector;
C(u, β) is an unknown Coherent Transfer Function amplitude;
φ(μ; α) is an unknown phase-aberration function; and
θ k (μ) is a known diversity phase function for channel k.
44. The method of claim 43 , where the amplitude aberration is given by
C
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45. The system of claim 22 , where in the processor-readable code configured to instruct the processor to estimate parameters to represent the object and phase and amplitude aberrations impacting the acquired images by applying a Coherent Transfer Function for the k th diversity channel given by:
H k ( u ; α, β)= C ( u ; β) e i[φ(u; α)+θ k (u)]
where:
k is the index of the phase diversity channel;
u is a two-dimensional spatial-frequency coordinate vector;
α is a phase-aberration parameter vector;
β is an Coherent Transfer Function amplitude-aberration parameter vector;
C(u; β) is an unknown Coherent Transfer Function amplitude;
φ(μ; α) is an unknown phase-aberration function; and
θ k (μ) is a known diversity phase function for channel k.
46. The method of claim 43 , where the amplitude aberration is given by
C
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47. The method of claim 29 , wherein said processing comprises a Coherent Transfer Function for the k th diversity channel given by:
H k ( u ; α, β)= C ( u ; β) e i[φ(u; α)+θ k (u)]
where:
k is the index of the phase diversity channel;
u is a two-dimensional spatial-frequency coordinate vector;
α is a phase-aberration parameter vector;
β is an Coherent Transfer Function amplitude-aberration parameter vector;
C(u; β) is an unknown Coherent Transfer Function amplitude;
φ(μ; α) is an unknown phase-aberration function; and
θ k (μ) is a known diversity phase function for channel k.
48. The method of claim 43 , where the amplitude aberration is given
C
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=
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β
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49. A method for imaging an object, the method comprising the steps of:
acquiring at least a first image and a second image of the object, the images being measurement-diverse;
estimating parameters to represent the object and at least amplitude aberrations impacting the acquired images;
calculating a measure of likelihood that the estimated parameters correspond to the object and at least amplitude aberrations in the acquired images; and
repeating said steps of estimating and calculating until the measure of likelihood is substantially maximized, wherein the estimated parameters are adjusted prior to each repetition and whereby said steps of estimating, calculating and repeating create an estimated image of the object.
50. The method of claim 49 , further comprising outputting parameters corresponding at least to the amplitude aberrations of the substantially maximized measure of likelihood and using the output parameters for the correction of an optical system.
51. A system for imaging an object, the system comprising:
a processor;
at least one JO interface electrically coupled to said processor;
at least one detector electrically coupled to said processor via the JO interface, the detector configured to acquire at least a first image and a second image of the object, the images being measurement-diverse; and
a memory device electrically coupled to said processor, said memory device including processor-readable code configured to instruct the processor to:
estimate parameters to represent the object and at least amplitude aberrations impacting the acquired images;
calculate a measure of likelihood that the estimated parameters correspond to the object and the at least amplitude aberrations impacting the acquired images; and
repeat the steps of estimation and calculation until the measure of likelihood is substantially maximized, wherein the estimated parameters are adjusted prior to each repetition and whereby the estimation, calculation and repetition create an estimated image of the object.
52. The system of claim 51 , further comprising outputting parameters corresponding to at least the amplitude aberrations of the substantially maximized measure of likelihood and using the output parameters for the correction of an optical system.
53. A method for imaging an object, the method comprising the steps of:
illuminating the object with a light source having a short coherence length such that the object appears to be incoherently illuminated;
acquiring image data for the object; and
processing the acquired image data to obtain an estimate of at least amplitude aberrations present in the acquired image data and create an estimated image of the object; wherein the image data acquired is measurement-diverse.
54. The method of claim 53 , further comprising:
outputting parameters to at least partially compensate for the amplitude aberrations; and
generating an image based at least partially on the image data and the parameters.