The Hartmann test is frequently performed with a screen with many holes to test the quality of a mirror or the aberrations of a lens. An application of the simplest form of this test with only four holes is described. This test cannot detect spherical aberration, but it may be useful to align optical systems, to detect and measure focus errors, or to detect lens decenterings and coma.
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Daniel Malacara-Hernández (1992) studied this question.