The passband integrationproperties of Birefringent filter

TL;DR

This paper investigates the photon conservation phenomenon in Birefringent filters used in solar observations, proposing it as a manifestation of the Parseval theorem with mathematical and experimental support.

Contribution

It provides a detailed analysis of photon conservation in Birefringent filters, linking it to the Parseval theorem and offering experimental and mathematical validation.

Findings

Photon count in the passband remains constant regardless of instrument transmittance.

The phenomenon is linked to the Parseval theorem in mathematical analysis.

Experimental observations support the photon conservation hypothesis.

Abstract

In this article, we discuss an observation phenomenon where the total amount of photons in the full passband of the Birefringent lter is a constant number that is considered by removing the spectrum of the light source irrespective of the instrument transmittance. This conclusion is only noticed and considered to be correct in Huairou Solar Observing Station since 1980s. This article will give a further discussion to the question that had been proposed by the previous researchers. The article structure is organized as history (Sec. 1), experiment (Sec. 2), math (Sec. 3), and discussion (Sec. 4). This issue should be the Paseval-Theorem manifesting itself in astronomical measurement, even though we rigorously demonstrate that this photons conservation has its mathematical generality in Sec. 3.