Multiplexed imaging
An imaging method comprises acquiring image data in which image components are spatially modulated at distinct spatial frequencies, transforming the image data into the Fourier domain and separating the image components in the Fourier domain. The image components may be transformed into the spatial domain. The image components may comprise different colors. In some embodiments saturated pixels are reconstructed by performing an optimization based on differences between image copies in the Fourier domain. Imaging apparatus may perform the imaging methods.
1. A method for obtaining image data, the method comprising:
acquiring image data by exposing an imaging array to optical radiation and operating the imaging array, wherein acquiring the image data comprises spatially modulating a response of the imaging array to each of a plurality of components of the optical radiation according to a corresponding basis function for an invertible transformation;
applying the transformation to the image data to yield transformed image data, the transformed image data comprising spatially-separated image copies corresponding respectively to the plurality of components;
extracting the spatially-separated image copies from the transformed image data; and
applying an inverse of the transformation to each of the extracted image copies;
wherein the modulation is spatially periodic and has a spatial frequency that is different for each of the components.
2. A method according to claim 1 wherein acquiring the image data comprises allowing the optical radiation to pass through an optical filter before interacting with pixels of the imaging array.
3. A method according to claim 2 wherein the optical filter has a spatial variation having at least first and second spatial frequencies.
4. A method according to claim 2 wherein the optical filter has a transmissivity in excess of 45%.
5. A method according to claim 1 wherein acquiring the image data comprises band-limiting a spatial frequency of the optical radiation prior to allowing the optical radiation to interact with the imaging array.
6. A method according to claim 1 wherein the basis functions comprise sinusoids.
7. A method according to claim 1 wherein acquiring the image data comprises spatially modulating a response of the imaging array to a first one of the plurality of components of the optical radiation according to a first sinusoid having a first spatial frequency and spatially modulating a response of the imaging array to a second one of the plurality of components of the optical radiation according to a second sinusoid having the first spatial frequency and a phase difference of ¼ wave with the first sinusoid.
8. A method according to claim 7 comprising extracting a pair of spatially-separated copies each corresponding to the first spatial frequency, computing a real part of a sum of the pair of spatially-separated copies and an imaginary part of a difference of the pair of spatially-separated copies, and applying the inverse of the transformation to the real part and the imaginary part.
9. A method for obtaining image data, the method comprising:
acquiring image data by exposing an imaging array to optical radiation and operating the imaging array, wherein acquiring the image data comprises allowing the optical radiation to pass through an optical filter before interacting with pixels of the imaging array and spatially modulating a response of the imaging array to each of a plurality of components of the optical radiation according to a corresponding basis function for an invertible transformation;
applying the transformation to the image data to yield transformed image data, the transformed image data comprising spatially-separated image copies corresponding respectively to the plurality of components;
extracting the spatially-separated image copies from the transformed image data; and
applying an inverse of the transformation to each of the extracted image copies;
wherein the optical filter has a spatial variation having at least first and second spatial frequencies
wherein the optical filter comprises tiles that repeat in a multiple of a pitch of pixels of the imaging array.
10. A method for obtaining image data, the method comprising:
acquiring image data by exposing an imaging array to optical radiation and operating the imaging array, wherein acquiring the image data comprises spatially modulating a response of the imaging array to each of a plurality of components of the optical radiation according to a corresponding basis function for an invertible transformation;
applying the transformation to the image data to yield transformed image data, the transformed image data comprising spatially-separated image copies corresponding respectively to the plurality of components;
extracting the spatially-separated image copies from the transformed image data; and,
applying an inverse of the transformation to each of the extracted image copies;
wherein the basis functions corresponding to the plurality of components are mutually orthogonal.
11. A method according to claim 10 wherein the components comprise primary colors.
12. A method according to claim 10 wherein the components comprise a red component a blue component and a green component and acquiring the image data comprises modulating each of the red, blue and green components at a distinct spatial frequency.
13. A method for obtaining image data, the method comprising:
acquiring image data by exposing an imaging array to optical radiation and operating the imaging array, wherein acquiring the image data comprises spatially modulating a response of the imaging array to each of a plurality of components of the optical radiation according to a corresponding basis function for an invertible transformation;
applying the transformation to the image data to yield transformed image data, the transformed image data comprising spatially-separated image copies corresponding respectively to the plurality of components;
extracting the spatially-separated image copies from the transformed image data; and
applying an inverse of the transformation to each of the extracted image copies;
wherein a direction of the spatial modulation is not aligned with rows or columns of the imaging array.
14. A method for obtaining image data, the method comprising:
acquiring image data by exposing an imaging array to optical radiation and operating the imaging array, wherein acquiring the image data comprises spatially modulating a response of the imaging array to each of a plurality of components of the optical radiation according to a corresponding basis function for an invertible transformation;
applying the transformation to the image data to yield transformed image data, the transformed image data comprising spatially-separated image copies corresponding respectively to the plurality of components;
extracting the spatially-separated image copies from the transformed image data; and
applying an inverse of the transformation to each of the extracted image copies;
wherein the components comprise polarization states.
15. An imaging array comprising a filter array having a plurality of first filter cells for a first spectral band and a plurality of second filter cells for a second spectral band, wherein filter transmissivities of the plurality of first filter cells for the first spectral band vary spatially with a first spatial frequency, and filter transmissivities of the plurality of second filter cells for the second spectral band vary spatially with a second spatial frequency, the first spatial frequency and the second spatial frequency being different.
16. An imaging array according to claim 15 wherein the transmissivity for each of the spectral bands varies sinusoidally.
17. An imaging array according to claim 15 wherein each of the first and second spectral bands comprises a band passing red light, a band passing blue light or a band passing green light.