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Signal-to-noise-ratio limit to the depth-of-field extension for imaging systems with an arbitrary pupil function.

Saeed Bagheri¹, Paulo E X Silveira, George Barbastathis

¹IBM T. J. Watson Research Center, 1101 Kitchawan Road, Room 11-209, Yorktown Heights, New York 10598, USA. sbagher@us.ibm.com

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|April 3, 2009

Summary

We found a fundamental limit to extending depth-of-field (DOF) in imaging systems. This limit involves a tradeoff between DOF extension and spectral signal-to-noise ratio (SNR), introducing a spectral SNR conservation principle.

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Area of Science:

Optical imaging systems
Aspheric optics
Image quality assessment

Background:

Depth-of-field (DOF) is crucial for imaging system performance.
Extending DOF often comes at the cost of other image quality metrics.
Previous studies have not rigorously defined the DOF extension limit in relation to spectral signal-to-noise ratio (SNR).

Purpose of the Study:

To rigorously derive the tradeoff between DOF extension and spectral SNR for imaging systems with arbitrary pupil functions.
To establish an upper bound for the minimum spectral SNR, defining the limit of DOF extension.
To introduce and define the spectral SNR conservation principle.

Main Methods:

Utilizing the relationship between the conservation of ambiguity and modulation-transfer function (MTF).
Applying the relationship between spectral SNR and MTF.
Deriving an expression for the upper bound of minimum spectral SNR.

Main Results:

A rigorous tradeoff between DOF extension and spectral SNR is established for the first time.
An upper bound for the minimum spectral SNR is derived, quantifying the limit of DOF extension.
The spectral SNR conservation principle is introduced.

Conclusions:

The study establishes a fundamental physical limit to DOF extension in imaging systems.
The spectral SNR conservation principle is presented as the spectral analog of the conservation of brightness theorem.
This work provides a theoretical framework for optimizing imaging systems with extended DOF.