SummaryWe present a technique to measure the wavefront in the exit pupil of a microscope to determine the microscope's threedimensional point spread function (PSF) experimentally. The wavefront yields the microscope PSF through a Fourier transform that models propagation of light from the exit pupil to the image plane. A Shack-Hartmann wavefront sensor is used to measure the wavefront shape by recording lateral displacements of a grid of focused spots created by a lenslet array. The displacement of each spot is related to the local wavefront slope. Thus, with appropriate sampling across the exit pupil, the entire wavefront can be reconstructed. This technique does not require the use of a sub-resolution object to obtain the three-dimensional microscope PSF. Consequently, larger, brighter fluorescent objects may be imaged, thereby reducing the requirements for detector sensitivity and leading to a three-fold increase in the axial range over which the PSF is measured. The Shack-Hartmann technique results in a description of the PSF as a continuous function whose sampling is not dependent on the size of the CCD pixels. The Shack-Hartmann sensor is not limited by the numerical aperture of the objective and can easily be calibrated to measure the PSF at any wavelength.

In this work, a model based method is applied to phase measuring deflectometry, named modal phase measuring deflectometry. The height and slopes of the surface under test are represented by mathematical models and updated by optimizing the model coefficients to minimize the discrepancy between the reprojection in ray tracing and the actual measurement. The pose of the screen relative to the camera is pre-calibrated and further optimized together with the shape coefficients of the surface under test. Simulations and experiments are conducted to demonstrate the feasibility of the proposed approach.

The correspondence residuals due to the discrepancy between the reality and the shape model in use are analyzed for the modal phase measuring deflectometry. Slope residuals are calculated from these discrepancies between the modal estimation and practical acquisition. Since the shape mismatch mainly occurs locally, zonal integration methods which are good at dealing with local variations are used to reconstruct the height residual for compensation. Results of both simulation and experiment indicate the proposed height compensation method is effective, which can be used as a post-complement for the modal phase measuring deflectometry.

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