Characterization of spatially varying aberrations for wide field-of-view microscopy

Abstract

We describe a simple and robust approach for characterizing the spatially varying pupil aberrations of microscopy systems. In our demonstration with a standard microscope, we derive the location-dependent pupil transfer functions by first capturing multiple intensity images at different defocus settings. Next, a generalized pattern search algorithm is applied to recover the complex pupil functions at ~350 different spatial locations over the entire field-of-view. Parameter fitting transforms these pupil functions into accurate 2D aberration maps. We further demonstrate how these aberration maps can be applied in a phase-retrieval based microscopy setup to compensate for spatially varying aberrations and to achieve diffraction-limited performance over the entire field-of-view. We believe that this easy-to-use spatially-varying pupil characterization method may facilitate new optical imaging strategies for a variety of wide field-of-view imaging platforms.

Fig. 1

Multi-plane phase retrieval with defocus diversity. (a) Multiple intensity images I(s) (s = −2, −1, 0, 1, 2) are captured at different defocus settings. (b) Multi-plane iterative phase retrieval algorithm presented in [29].

Fig. 2

Pupil function recovery at one off-axis position. Two cropped areas of one set of defocused intensity images are used for algorithm input. One cropped set I_c(s) is centered on a microsphere at the images’ central FOV (left), while the other cropped set I_d(s) is centered on a microsphere at an off-axis position (right). Each cropped image set contains 17 intensity measurements (here only 5 are shown) at different defocus distances (−400 µm to + 400 µm, 50 µm per step). We approximate an unknown pupil function W with 8 Zernike coefficients (x-tilt, y-tilt, x-astigmatism, y-astigmatism, defocus, x-coma, y-coma and spherical aberration). We use this pupil function estimate to modify the 17 “ground truth” images I_c(s) of the central microsphere to generate a new set of aberrated intensity images, I_a(s) (middle). We then adjust the values of the 8 unknown Zernike coefficients to minimize the difference between I_a(s) and the actual intensity measurements of the off-axis microsphere, I_d(s) (right). The corresponding pupil function described by 8 Zernike coefficients is recovered when the mean-squared error difference between these two image sets is minimized.

Fig. 3

Off-axis aberration characterization with a calibration target. (a) ~350 microspheres are automatically identified on a microscope slide, each denoted by a red dot. (b) The recovered pupil function at position (x₁, y₁). (c1)-(c5) Intensity measurements I_d(s) of the microsphere centered at (x₁, y₁) under different amounts of defocus. (d1)-(d5) The corresponding aberrated image estimates generated using the pupil function in Fig. 3(b).

Fig. 4

Spatially varying aberrations of the 2X objective lens. Each data point, denoted by a blue dot, represents the extracted Zernike coefficient weight for one microsphere. ~350 microspheres are identified over the entire FOV and their corresponding parameters are fitted to a 2D surface for each type of aberration. (a)-(f) correspond to x-astigmatism, y-astigmatism defocus, x-coma, y-coma and spherical aberration.

Fig. 5

Recovered defocus parameter function p₅(x, y) with (color surface) and without (blue grid) +50 µm of sample defocus. The difference between these two surfaces corresponds to a defocus distance of +48.9 µm, which is in a good agreement with the actual displacement distance.

Fig. 6

Resolution characterization using a USAF resolution target. (a) The USAF resolution target is placed at 3 different locations indicated by color arrows (b)-(d). Full FOV corresponds to circular region with 1.3 cm diameter. The original images captured using the aberrated objective lens at the center (b1), 60% away from the center (c1), and 95% away from the center (d1). (b2)-(d2) are the corresponding processed images using the deconvolution scheme. Group 7, element 1 (line width of 3.9 µm) of the USAF target can be resolved from the corrected images, in a good agreement with the Abbe diffraction limit of 3.94 µm.

Fig. 7

Full FOV image deconvolution of the microsphere calibration target. (a) The aberration-corrected full FOV image. (b1)-(e1) Recovered pupil functions corresponding to highlighted regions in (a). (b2)-(e2) The corrected images of highlighted regions in (a). (b3)-(e3) The original images of the test target without aberration correction.

Fig. 8

Full FOV image deconvolution of a new test target, containing a mixture of microspheres with different diameters (5-20 µm). (a) The aberration-corrected full FOV image. (b1)-(e1) Recovered pupil functions corresponding to highlighted regions in (a). (b2)-(e2) The corrected images of highlighted regions in (a). (b3)-(e3) The original images of the test target without aberration correction.