Material testing by angle-variable illumination
An optical system includes an illumination module configured to illuminate a sample object with at least one angle-variable illumination geometry. The optical system includes an imaging optical unit configured to produce an imaged representation of the sample object that is illuminated with the at least one angle-variable illumination geometry on a detector. The optical system includes the detector, which is configured to capture at least one image of the sample object based on the imaged representation. The optical system includes a controller configured to determine a result image based on a transfer function and the at least one image. A method includes illuminating a sample object with at least one angle-variable illumination geometry, imaging the sample object on a detector, based on the imaged representation, capturing at least one image of the sample object, and, based on a transfer function and the at least one image, determining a result image.
1. An optical system comprising:
an illumination module configured to illuminate a sample object with at least one pair of angle-variable illumination geometries corresponding to different illumination directions, thus implementing an illumination structured in angle space;
an imaging optical unit configured to produce an imaged representation of the sample object that is illuminated with the at least one pair of angle-variable illumination geometries on a detector;
the detector, wherein the detector is configured to capture at least one pair of real-space images of the sample object based on the imaged representation; and
a controller configured to:
determine a transfer function based on the at least one pair of angle-variable illumination geometries;
determine a pairwise difference for each pair of the at least one pair of real-space images;
determine a spectral decomposition of the pairwise difference; and
determine a real-space result image based on the transfer function and the spectral decomposition.
2. The optical system of claim 1 , wherein the illumination module and the detector are arranged in reflected light geometry.
3. The optical system of claim 1 , wherein the illumination module is configured to illuminate the sample object in dark field geometry.
4. The optical system of claim 1 , wherein:
the controller is configured to detect anomalies in the real-space result image and
the anomalies comprise extreme values in contrast of the real-space result image.
5. The optical system of claim 1 , wherein:
the controller is configured to detect anomalies in the real-space result image and
the anomalies comprise deviations from a real-space pattern of the sample object.
6. The optical system of claim 5 , wherein the controller is configured to determine the deviations from the real-space pattern of the sample object based on at least one of the following techniques: Fourier space filtering, autocorrelation, and deviations with respect to a reference image of the real-space pattern.
7. The optical system of claim 1 , wherein:
the imaging optical unit is characterized by an aperture size, N A ;
a lower threshold is defined based on 5% of a maximum value of all absolute values of the transfer function for spatial frequencies between —N A and N A ; and
for spatial frequencies between —N A and N A , each absolute value of the transfer function is greater than the lower threshold.
8. The optical system of claim 1 , wherein:
the imaging optical unit is characterized by an aperture size, N A ;
a lower threshold is defined based on 2% of a maximum value of all absolute values of the transfer function for spatial frequencies between —N A and N A ; and
for spatial frequencies between —N A and N A , each absolute value of the transfer function is greater than the lower threshold.
9. The optical system of claim 1 , wherein:
the imaging optical unit is characterized by an aperture size, N A ;
a lower threshold is defined based on 0.5% of a maximum value of all absolute values of the transfer function for spatial frequencies between — 2N A and 2N A ; and
for spatial frequencies between — 2N A and 2N A , each absolute value of the transfer function is greater than the lower threshold.
10. The optical system of claim 1 , wherein:
the imaging optical unit is characterized by an aperture size, N A and for spatial frequencies between —N A and N A , the transfer function has no local extreme values.
11. The optical system of claim 1 , wherein the transfer function is a step function.
12. The optical system of claim 1 , wherein the transfer function is one of a monotonously increasing function and a monotonously decreasing function.
13. The optical system of claim 12 , wherein the transfer function is at least one of a linear function and a sigmoid function.
14. The optical system of claim 1 , wherein the transfer function has an axis of symmetry that corresponds to an axis of symmetry of the at least one pair of angle-variable illumination geometries.
15. The optical system of claim 1 , wherein:
the imaging optical unit is characterized by an aperture size, N A ;
an upper threshold is defined based on 5% of a maximum value of all absolute values of the transfer function for spatial frequencies between —N A and N A ; and
for spatial frequencies greater than 2N A and for spatial frequencies less than — 2N A , each absolute value of the transfer function is less than the upper threshold.
16. The optical system of claim 1 , wherein:
the imaging optical unit is characterized by an aperture size, N A ;
an upper threshold is defined based on 2% of a maximum value of all absolute values of the transfer function for spatial frequencies between — 2N A and 2N A ; and
for spatial frequencies greater than 2N A and for spatial frequencies less than — 2N A , each absolute value of the transfer function is less than the upper threshold.
17. The optical system of claim 1 , wherein:
the imaging optical unit is characterized by an aperture size, N A ;
an upper threshold is defined based on 0.5% of a maximum value of all absolute values of the transfer function for spatial frequencies between —N A and N A ; and
for spatial frequencies greater than N A and for spatial frequencies less than —N A , each absolute value of the transfer function is less than the upper threshold.
18. The optical system of claim 1 , wherein the controller is configured to determine the real-space result image based on a Tikhonov regularization with inverse Fourier transform.
19. A method comprising:
illuminating a sample object with at least one pair of angle-variable illumination geometries corresponding to different illumination directions, thus implementing an illumination structured in angle space;
producing an imaged representation of the sample object illuminated with the at least one pair of angle-variable illumination geometries on a detector;
based on the imaged representation, capturing at least one pair of real-space images of the sample object;
determining a transfer function based on the at least one pair of angle-variable illumination geometries;
a pairwise difference of the at least one pair of real-space images;
determining a spectral decomposition of the pairwise difference; and
based on the transfer function and the spectral decomposition, determining a real-space result image.
20. The optical system of claim 1 , wherein the transfer function designates a transfer function other than an object transfer function or an optics transfer function.
21. The optical system of claim 1 , wherein the controller is configured to:
determine a ratio of (i) a difference of each pair of the at least one pair of real-space images to (ii) a sum of the two images of the respective pair; and
determine the real-space result image based on the transfer function and the ratio.