Singer product apertures
View Patent ↗A coded aperture mask is provided. The coded aperture mask may include a 2-D planar substrate having a plurality of holes constructed based on a Cartesian product of a first 1-D aperture set and a second 1-D aperture set. The first 1-D aperture set may have a first balanced decoder. The second 1-D aperture set may have a second balanced decoder. The Cartesian product may involve the first 1-D aperture set and the second 1-D aperture set arranged in a non-zero angle (e.g., 90 degrees) to each other. The first 1-D aperture set may define a first axis of the 2-D planar substrate. The second 1-D aperture set may define a second axis of the 2-D planar substrate. The plurality of holes on the 2-D planar substrate may correspond to holes in both of the first 1-D aperture set and the second 1-D aperture set.
1. A coded aperture mask comprising:
a 2-dimensional planar substrate having a plurality of holes constructed based on a Cartesian product of a first 1-dimensional aperture set and a second 1-dimensional aperture set,
wherein the first 1-dimensional aperture set has a first non-unimodular balanced decoder,
wherein the second 1-dimensional aperture set has a second non-unimodular balanced decoder,
wherein the Cartesian product involves the first 1-dimensional aperture set and the second 1-dimensional aperture set arranged in a non-zero angle to each other, the first 1-dimensional aperture set defining a first axis of the 2-dimensional planar substrate, the second 1-dimensional aperture set defining a second axis of the 2-dimensional planar substrate, wherein the plurality of holes correspond to holes in both of the first 1-dimensional aperture set and the second 1-dimensional aperture set; and
wherein a first cyclic, correlation between the first non-unimodular balanced decoder and the first 1-dimensional aperture set has identically zero sidelobes, wherein a second cyclic correlation between the second non-unimodular balanced decoder and the second 1-dimensional aperture set has identically zero sidelobes.
2. The coded aperture mask of claim 1 , wherein the first 1-dimensional aperture set has a first open fraction, the first open fraction being a first ratio of a number of holes in the first 1-dimensional aperture set to a total number of pixels in the first 1-dimensional aperture set, wherein the second 1-dimensional aperture set has a second open fraction, the second open fraction being a second ratio of a number of holes in the second 1-dimensional aperture set to a total number of pixels in the second 1-dimensional aperture set.
3. The coded aperture mask of claim 1 , wherein each of the first 1-dimensional aperture set and the second 1-dimensional aperture set is one of a Singer set, a quadratic residue set, a biquadratic residue set, or an octic residue set.
4. The coded aperture mask of claim 1 , wherein each of the first 1-dimensional aperture set and the second 1-dimensional aperture set is chosen from a family of sets that possess balanced decoders or products of the family of sets unwrapped to make the products 1-dimensional.
5. The coded aperture mask of claim 1 , wherein the non-zero angle is 90 degrees.
6. A method of coded aperture imaging, the method comprising:
receiving an image formed on a detector by radiation passed through a coded aperture mask, the image comprising a plurality of rows and a plurality of columns,
wherein the coded aperture mask comprises a 2-dimensional planar substrate having a plurality of holes constructed based on a Cartesian product of a first 1-dimensional aperture set and a second 1-dimensional aperture set, wherein the first 1-dimensional aperture set has a first non-unimodular balanced decoder, wherein the second 1-dimensional aperture set has a second non-unimodular balanced decoder; and
decoding the image based on the first 1-dimensional aperture set and the second 1-dimensional aperture set;
wherein a first cyclic correlation between the first non-unimodular balanced decoder and the first 1-dimensional aperture set has identically zero sidelobes, wherein a second cyclic correlation between the second non-unimodular balanced decoder and the second 1-dimensional aperture set has identically zero sidelobes.
7. The method of claim 6 , wherein the Cartesian product involves the first 1-dimensional aperture set and the second 1-dimensional aperture set arranged in a non-zero angle to each other, the first 1-dimensional aperture set defining a first axis of the 2-dimensional planar substrate, the second 1-dimensional aperture set defining a second axis of the 2-dimensional planar substrate, wherein the plurality of holes correspond to holes in both of the first 1-dimensional aperture set and the second 1-dimensional aperture set, wherein the non-zero angle is 90 degrees.
8. The method of claim 6 , wherein the first 1-dimensional aperture set has a first open fraction, the first open fraction being a first ratio of a number of holes in the first 1-dimensional aperture set to a total number of pixels in the first 1-dimensional aperture set, wherein the second 1-dimensional aperture set has a second open fraction, the second open fraction being a second ratio of a number of holes in the second 1-dimensional aperture set to a total number of pixels in the second 1-dimensional aperture set, wherein each of the first open fraction and the second open fraction is adjustable in a range between 0 and 0.5.
9. The method of claim 6 , wherein each of the first 1-dimensional aperture set and the second 1-dimensional aperture set is one of a Singer set, a quadratic residue set, a biquadratic residue set, or an octic residue set.
10. The method of claim 6 , wherein each of the first 1-dimensional aperture set and the second 1-dimensional aperture set is chosen from a family of sets that possess balanced decoders or products of the family of sets unwrapped to make the products 1-dimensional.
11. The method of claim 6 , wherein the decoding of the image comprises:
applying the first balanced decoder to one of the plurality of rows or the plurality of columns; and
applying the second balanced decoder to the other of the plurality of rows or the plurality of columns.
12. The method of claim 6 , wherein the decoding of the image comprises:
applying the first 1-dimensional aperture set as a first direct decoder to one of the plurality of rows or the plurality of columns;
applying the second 1-dimensional aperture set as a second direct decoder to the other of the plurality of rows or the plurality of columns to obtain an intermediate decoded image; and
adjusting image pixel brightness of the intermediate decoded image by adding or subtracting from each pixel value a first multiple of a first sum on a first dimension of the intermediate decoded image corresponding to the pixel value, a second multiple of a second sum on a second dimension of the intermediate decoded image corresponding to the pixel value, and a third multiple of a total number of tracks on the detector.
13. A method of coded aperture imaging, the method comprising:
determining a number of pixels in an object being imaged;
calculating a target open fraction based on the number of pixels; and
selecting a coded aperture mask for imaging the object based on the target open fraction:
wherein the coded aperture mask comprises a 2-dimensional planar substrate having a plurality of holes constructed based on a Cartesian product of a first 1-dimensional aperture set and a second 1-dimensional aperture set, wherein the first 1-dimensional aperture set has a first non-unimodular balanced decoder, wherein the second 1-dimensional aperture set has a second non-unimodular balanced decoder, and
wherein a first cyclic correlation between the first non-unimodular balanced decoder and the first 1-dimensional aperture set has identically zero sidelobes, wherein a second cyclic correlation between the second non-unimodular balanced decoder and the second 1-dimensional aperture set has identically zero sidelobes.
14. The method of claim 13 , wherein the Cartesian product involves the first 1-dimensional aperture set and the second 1-dimensional aperture set arranged in a non-zero angle to each other, the first 1-dimensional aperture set defining a first axis of the 2-dimensional planar substrate, the second 1-dimensional aperture set defining a second axis of the 2-dimensional planar substrate, wherein the plurality of holes correspond to holes in both of the first 1-dimensional aperture set and the second 1-dimensional aperture set, wherein the non-zero angle is 90 degrees.
15. The method of claim 13 , wherein the first 1-dimensional aperture set has a first open fraction, the first open fraction being a first ratio of a number of holes in the first 1-dimensional aperture set to a total number of pixels in the first 1-dimensional aperture set, wherein the second 1-dimensional aperture set has a second open fraction, the second open fraction being a second ratio of a number of holes in the second 1-dimensional aperture set to a total number of pixels in the second 1-dimensional aperture set.
16. The method of claim 15 , wherein the selecting of the coded aperture mask comprises:
selecting the first 1-dimensional aperture set so that the first open fraction is closest to the target open fraction; and
selecting the second 1-dimensional aperture set so that the second open fraction is closest to the target open fraction.
17. The method of claim 13 , wherein each of the first 1-dimensional aperture set and the second 1-dimensional aperture set is one of a Singer set, a quadratic residue set, a biquadratic residue set, or an octic residue set.
18. The method of claim 13 , wherein each of the first 1-dimensional aperture set and the second 1-dimensional aperture set is chosen from a family of sets that possess balanced decoders or products of the family of sets unwrapped to make the products 1-dimensional.