Determining optical aberration

1 . A method of determining aberration in an optical system, the optical system comprising an adaptive optical element, the method comprising:

a) obtaining a first image in which the adaptive optical element is in a first configuration;

b) obtaining a second image in which the adaptive optical element is in a second configuration, wherein the second configuration is different from the first configuration;

c) applying a transform to the first image and the second image to produce a transformed first image and a transformed second image;

d) obtaining a ratio comprising the transformed first image and the transformed second image and determining a pseudo-point spread function (pseudo-PSF) from the ratio; and

e) providing data sampled from the pseudo-PSF to a machine learning algorithm that has been trained to determine an output indicative of aberration coefficients from the data.

2 . The method of claim 1 , wherein:

in the first configuration the adaptive optical element is configured to introduce a first phase aberration comprising at least one non-zero Zernike polynomial coefficient with a Noll index greater than 4; and

in the second configuration the adaptive optical element is configured to introduce a second phase aberration, wherein the second phase aberration is different from the first phase aberration.

3 . The method of claim 2 , wherein:

i) the first phase aberration is or comprises astigmatism; and/or

ii) the second phase aberration is zero; or

iii) the second phase aberration is an aberration having opposite polarity or amplitude to the first phase aberration.

4 . The method of claim 2 , wherein:

obtaining the first image comprises obtaining a plurality of first images in each of which the adaptive optical element is configured to introduce a different first phase aberration comprising at least one non-zero Zernike polynomial coefficient with a Noll index greater than 4; and

obtaining the second image comprises obtaining a plurality of second images.

5 . The method of claim 2 , wherein:

obtaining the first image comprises obtaining a first image in which the adaptive optical element is configured to introduce a plurality of first phase aberrations, at least one of the first phase aberrations comprising at least one non-zero Zernike polynomial coefficient with a Noll index greater than 4; and

obtaining the second image comprises obtaining a second image in which the adaptive optical element is configured to introduce a plurality of second phase aberrations different from the plurality of first phase aberrations.

6 . The method of claim 1 , wherein determining the pseudo-PSF comprises applying the inverse of the transform to determine a pseudo-PSF image from the ratio.

7 . The method of claim 1 , wherein the transform comprises the property that a convolution in the image domain is transformed to a multiplication in the transformed domain.

8 . The method of claim 7 , wherein the transform is one of a Fourier transform, a Fourier cosine transform, a Fourier sine transform or a wavelet transform.

9 . The method of claim 1 , wherein:

obtaining the ratio comprises obtaining a first ratio of the transformed first image to the transformed second image and obtaining a second ratio of the transformed second image to the transformed first image; and

determining the pseudo-PSF comprises determining a first pseudo-PSF from the first ratio and determining a second pseudo-PSF from the second ratio.

10 . The method of claim 1 , wherein:

in the first configuration the adaptive optical element is configured to generate a first plurality of focal spots having a first arrangement; and

in the second configuration the adaptive optical element is configured to generate a second plurality of focal spots having a second arrangement, wherein the second arrangement of focal spots is different from the first arrangement of focal spots.

11 . The method of claim 10 , wherein the focal spots are spaced apart from one another by a distance of the order of a width of the focal spots.

12 . The method of claim 10 , wherein at least one of the focal spots introduces a phase aberration, and optionally wherein each of a plurality of the focal spots introduce a different phase aberration.

13 . The method of claim 1 , wherein:

obtaining the first image comprises obtaining a plurality of first images simultaneously; and

obtaining the second image comprises obtaining a plurality of second images simultaneously.

14 . The method of claim 13 , wherein:

obtaining the plurality of first images simultaneously and obtaining the plurality of second images simultaneously comprises using a plurality of detectors located at different spatial locations or positions, optionally located at different lateral X-Y positions and/or at different Z positions or focal planes.

15 . The method of claim 1 , further comprising controlling the adaptive optical element based on the output from the machine learning algorithm to compensate or correct aberration in the optical system.

16 . The method of claim 15 , further comprising repeating steps a) to e) after controlling the adaptive optical element to compensate or correct aberration in the optical system.

17 . The method of claim 1 , wherein the machine learning algorithm comprises a series of convolution layers, each connected to a pooling operation.

18 . The method of claim 17 , wherein an output of each of the pooling operations is provided to a fully connected layer.

19 . A system comprising:

an optical system comprising an adaptive optical element; and

a processor operably connected to the optical system and configured to perform a method comprising the following steps:

a) obtaining a first image in which the adaptive optical element is in a first configuration;

b) obtaining a second image in which the adaptive optical element is in a second configuration, wherein the second configuration is different from the first configuration;

c) applying a transform to the first image and the second image to produce a transformed first image and a transformed second image;

d) obtaining a ratio comprising the transformed first image and the transformed second image and determining a pseudo-point spread function (pseudo-PSF) from the ratio; and

e) providing data sampled from the pseudo-PSF to a machine learning algorithm that has been trained to determine an output indicative of aberration coefficients from the data.

20 . A non-transitory computer readable medium storing a computer program comprising instructions which, when the program is executed by a processor, cause the processor to carry out a method comprising the following steps:

a) obtaining a first image in which the adaptive optical element is in a first configuration;

b) obtaining a second image in which the adaptive optical element is in a second configuration, wherein the second configuration is different from the first configuration;

c) applying a transform to the first image and the second image to produce a transformed first image and a transformed second image;

d) obtaining a ratio comprising the transformed first image and the transformed second image and determining a pseudo-point spread function (pseudo-PSF) from the ratio; and

e) providing data sampled from the pseudo-PSF to a machine learning algorithm that has been trained to determine an output indicative of aberration coefficients from the data.