Microscopy: Differentiable model-based adaptive optics with transmitted and reflected light

• Improves resolution and intensity of the image in an efficient way
• Needs a small number of measurements for finding aberration corrections
• Suitable for epi-detection configurations

• Laser scanning microscopy
• Biological imaging

Machine learning offers novel approaches to correct for aberrations encountered when imaging through scattering materials with transmitted and reflected light. However, for training a neural network large datasets are required, because the parameters of the neural network need to be adjusted i) to work under a wide range of conditions and ii) to learn the underlying image generat-ing process through the optical system. The training dataset can be reduced, if information about the image generation process is a priori known. However, training datasets are often based on combinations of Zernike polynomials and hence might not accurately capture all aspects of the aberrations. Additionally, for strongly scattering samples higher orders of Zernike modes are required, which further increases the training dataset. Therefore, for at least those optical sys-tems for which a priori information of the image generation process is known, an improved meth-od for determining/correcting the aberrations in the optical system is needed.

The method uses a model of the optical system, which describes the light propagation through the optical system as a differentiable function. The model also includes unknown parameters, which account for aberrations occurring in the system and which are to be determined. For determining the unknown aberrations/parameters a number of output images resulting from corresponding input phase modulations are recorded and the unknown parameters are adjusted so that the input-output relationship of the computational model and the experimental setup match. Once the aberration pattern in the optical system is determined, the aberrations can be corrected by setting a complementary aberration pattern into the excitation path of the optical system; which can be done, for instance, by means of a spatial light modulator.

A microscope, employing the method according to the invention, is depicted in Fig. 1. In the microscope an expanded and collimated laser beam is reflected off a spatial light modulator (SLM) with a beam splitter cube BS1 and a part of the beam is imaged onto a transmission camera over a beam splitter BS3. For experiments with reflected light, the remaining part of the beam is additionally sent to a mirror at the sample plane (having the same focal plane as the transmission camera). The mirror serves as a proxy for a reflecting sample. Light reflected by the mirror is imaged onto a reflection camera with a beam splitter BS2. Aberrations are introduced between BS2 and BS3 by means of a scattering element A. The microscope can determine the aberration A by: a) providing a physical, mathematical differentiable model on a computer; b) irradiating an input light distribution I₀ by the collimated laser beam into the excitation path of the microscope; c) scattering the light I₀ with the scattering element A, thereby transforming I₀ to form the transmission light distribution I_TR; d) recording the light I_TR by means of the transmission camera; e) transferring the recorded light distribution I_TR to the model; and f) calculating transmission distortion parameters V_TR of the model based on the recorded distribution I_TR, wherein the parameters V_TR describe the aberrations introduced by the scattering element A in the excitation path.

Also, the microscope can determine the aberration A by: performing the above-mentioned steps a) to c); reflecting the light distribution I_TR by the mirror M; scattering the reflected light I_TR with element A to generate the reflection light distribution I_RE; recording the distribution I_RE with the reflection camera; transferring the recorded I_RE to the model; and calculating reflection distortion parameters V_RE of the model based on I_RE. The microscope can correct the aberrations A by setting a distortion pattern V*_TR or a pattern V*_RE on the SLM, wherein V*_TR and V*_RE are based on the determined parameters V_TR and V_RE, respectively. Examples of such corrections are shown in Fig. 2.

• DE 10 2020 119 566 A1
• WO 2022/018002 A1

Ivan Vishniakou and Johannes D. Seelig, Differentiable model-based adaptive optics with transmitted and reflected light, Optics Express, Vol. 28, No. 18 / 31 August 2020 / 26436