Abstract
An image-based technique for measuring the complex field in the pupil of an imaging system is presented. Two point source images, one with a small modification introduced in the pupil, are combined using a simple and non-iterative algorithm. The non-interferometric method is based on the change in the optical transfer function (OTF) giving a differential optical transfer function (dOTF). The dOTF includes two images of the complex pupil field, conjugated and reflected about the position of the pupil modification, leaving an overlap that obscures some of the pupil. The overlap can be minimized by introducing the modification near the edge of the pupil. The overlap region can be eliminated altogether by using a second modification and a third point source image. The pupil field is convolved by the change in the pupil field, so smaller modification areas are preferred. When using non-monochromatic light, the dOTF incurs a proportional radial blurring determined by the fractional bandwidth. We include some simple demonstration experiments, including using a pupil blockage and moving a single deformable mirror actuator as the pupil modification. In each case, the complex wavefront is easily recovered, even when the pupil mask is unknown and the wavefront aberrations are large.
Highlights
In a system where the point spread function (PSF) is shifted invariantly across the field, the incoherent object and image intensities are related by convolution with the PSF
If a third PSF is acquired with a second pupil modification near some other part of the pupil’s edge, the new overlap region will be located at a different place and the pair of differential optical transfer function (dOTF) images can be combined to retrieve the field at all points across the pupil
The dOTF method is a new and remarkably simple way to measure the complex amplitude of the pupil field in an optical system, including aberrations and transmission effects that occur between the pupil and the imaging sensor
Summary
In a system where the point spread function (PSF) is shifted invariantly across the field, the incoherent object and image intensities are related by convolution with the PSF. The OTF and its constituent functions are often used to characterize shortcomings of an optical system, they would be more diagnosed if the aberrated or vignetted pupil field were known instead of just the OTF It is a matter of knowing cause versus effect. This article presents a new technique for measuring the complex field in the pupil plane from the difference between the Fourier transform of two PSF images [differential optical transfer function (dOTF)]. If a third PSF is acquired with a second pupil modification near some other part of the pupil’s edge, the new overlap region will be located at a different place and the pair of dOTF images can be combined to retrieve the field at all points across the pupil.
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