Cramér-Rao sensitivity limits for astronomical instruments: implications for interferometer design.

Area of Science:

• Astronomy and Astrophysics
• Optical and Infrared Astronomy

Background:

• Multiple-telescope interferometry is crucial for high-angular-resolution imaging across optical, infrared, and far-infrared bands.
• Understanding instrument sensitivity is key to advancing astronomical observation capabilities.

Purpose of the Study:

• To review the fundamental principles governing the sensitivity of direct-detection instruments and interferometers.
• To discuss the rigorous sensitivity limits imposed by the Cramér-Rao theorem.
• To argue for interferometer designs that enhance sensitivity through spatial information extraction.

Main Methods:

• Review of fundamental principles of direct-detection instruments and interferometers.
• Discussion of sensitivity limits based on the Cramér-Rao theorem.
• Numerical calculations of the Cramér-Rao limit for a simplified case.

Main Results:

• Sensitivity limits for interferometric instruments were rigorously analyzed using the Cramér-Rao theorem.
• Numerical calculations demonstrated the impact of beam pattern compactness on sensitivity.
• Interferometers with more compact instantaneous beam patterns show increased sensitivity.

Conclusions:

• More compact beam patterns allow interferometers to extract more spatial information per detected photon, enhancing sensitivity.
• Arrays with a larger number of telescopes are favored for improved sensitivity.
• All-on-one beam-combining methods are preferable to pairwise combination for maximizing sensitivity.