Investigation of noise amplification questions in satellite jitter detected from CCDs’ parallax observation imagery: A case for 3 CCDs

Abstract

Parallax observations from adjacent CCDs have been applied to detect satellite jitter, and the highest detectable jitter frequency reaches up to half CCDs image line frequency, among which, however, not all frequencies’ jitter could be detected accurately. Jitter error mainly comes from the noise in offset data. In this research, it is found that at some frequencies the noise is amplified significantly, leading to seriously deviated jitter components and even unreliable jitter results. This research focuses on the noise-amplifying questions in jitter detection and explores what CCD parameters determine them. Firstly, the error transfer coefficients (ETC) between jitter and offset is derived, and the frequencies are divided into three categories: blind frequencies, noise-amplifying frequencies and noise-suppressing frequencies. Secondly, for two adjacent CCDs, formulas are established to determine their blind frequencies and noise-amplifying bands, which indicate that it is the two CCDs’ image line time tr and the distance l between the two CCDs’ first lines that determine their blind frequencies and noise-amplifying bands. The reciprocal of the product of tr and l is defined as the fundamental frequency F of the CCD pair. As a result, the blind frequencies and noise-amplifying bands both reoccur with a period of fundamental frequency F, but unlike those isolated bind frequencies, the noise-amplifying bands span much wider, up to nearly 1/3 jitter bandwidth. Thirdly, for three adjacent CCDs forming two CCD pairs, aliasing between the two pairs’ noise-amplifying bands is first proven to be inevitable and reoccurs in cycles. Formulas are then established to extract the aliasing components and compute the aliasing period length. Experiments and simulations are conducted to test the constructed theories. Results show that the RMSE is 7.127 ×10−5Hz for blind frequencies formulas, and the RRMSEs are 0.0051% for noise-amplifying bands’ period formulas, 0.0033% for aliasing period, and 1.2610% for noise-amplifying bandwidth, proving that the established formulas could generate reliable results for the blind frequencies, noise-amplifying bands and their aliasing components of three adjacent CCDs. Our studies are expected to help analyze more CCDs’ noise-amplifying problems and provide a prospect to reduce their impact on jitter detection by optimizing CCD parameter values.