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Deriving the Coltman Correction for Transforming the Bar Transfer Function to the Optical Transfer Function (or the

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Summary

The Coltman series was mathematically derived to calculate optical transfer function from bar transfer function measurements. This method is valid even with phase reversal in images.

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Area of Science:

Optics
Image Science
Metrology

Background:

Accurate measurement of the optical transfer function (OTF) is crucial for characterizing imaging systems.
Existing methods may face limitations when dealing with phase reversal in image data.

Purpose of the Study:

To mathematically derive the Coltman series for OTF calculation.
To define the bar transfer function (BTF) in a way that accommodates phase reversal.

Main Methods:

Mathematical derivation of the Coltman series.
Definition of the bar transfer function (BTF) as the primary measurement basis.

Main Results:

Successful mathematical derivation of the Coltman series.
Establishment of a valid relation between BTF and OTF, even with phase reversal.

Conclusions:

The derived Coltman series provides a robust method for OTF determination.
The BTF-based approach enhances the applicability of OTF measurements in diverse imaging scenarios.