Imaging performance of annular apertures. 4: Apodization and point spread functions

Area of Science:

• Optics and Photonics
• Image Science

Background:

• Point spread functions (PSFs) are crucial for understanding image quality.
• Apodization and central obstructions are optical techniques that modify light transmission.
• Previous studies have explored PSF modifications but less on combined effects and resulting irradiance distributions.

Purpose of the Study:

• To investigate how apodizations with decreasing transmissions and central obstructions affect point spread functions.
• To characterize the resulting image irradiance distributions using envelope functions.
• To explore the formation of new radial zones at high apodization levels and low central obstructions.

Main Methods:

• Mathematical modeling of apodizations with varying transmission profiles.
• Analysis of optical transfer functions and point spread functions.
• Characterization of image irradiance distributions using exponential envelope functions.

Main Results:

• Apodizations with decreasing transmission and central obstructions significantly alter PSF size and irradiance distribution.
• Envelope functions, characterized by descending exponential functions with variable exponents, describe these distributions.
• High apodization levels combined with low central obstruction (<0.1) create new extended radial zones in the outer regions of central ring groups.

Conclusions:

• The observed transmutations of image functions are significant for practical applications.
• The formation of new radial zones has implications for comparing image irradiance to background levels.
• These findings are relevant for advanced optical imaging systems and image analysis techniques.