#' Rho from pixels to arcseconds
#'
#' Convert rho from pixels to arcseconds for given band
#'
#' @param rho_px rho in px.
#' @param rho_px_err error of rho in px.
#' @param band a character string with band ('550', 600', '676', '694', '800', '850').
#' @return List with rho and it's error in arcseconds.
#' @examples
#' speckle_rho(rho_px = 12.1685, rho_px_err = 0.0865, band = '800')
#' @export
speckle_rho <- function(rho_px = NULL, rho_px_err = NULL, band = NULL) {
base_550 <- 0.00885267819
base_550_err <- 5.16421857e-05
q_600 <- 0.99651
q_600_err <- 0.00030
q_676 <- 0.99637
q_676_err <- 0.00043
q_694 <- 0.99556
q_694_err <- 0.00054
q_800 <- 0.98751
q_800_err <- 0.00059
q_850 <- 0.98982
q_850_err <- 0.00078
rho_sec_550 <- rho_px * base_550
rho_sec_err_550 <- rho_sec_550 * (base_550_err / base_550 + rho_px_err / rho_px)
if (band == '550') {
rho_sec <- rho_sec_550
rho_sec_err <- rho_sec_err_550
}
if (band == '600') {
rho_sec <- rho_sec_550 * q_600
rho_sec_err <- rho_sec * (rho_sec_err_550 / rho_sec_550 + q_600_err / q_600)
}
if (band == '676') {
rho_sec <- rho_sec_550 * q_676
rho_sec_err <- rho_sec * (rho_sec_err_550 / rho_sec_550 + q_676_err / q_676)
}
if (band == '694') {
rho_sec <- rho_sec_550 * q_694
rho_sec_err <- rho_sec * (rho_sec_err_550 / rho_sec_550 + q_694_err / q_694)
}
if (band == '800') {
rho_sec <- rho_sec_550 * q_800
rho_sec_err <- rho_sec * (rho_sec_err_550 / rho_sec_550 + q_800_err / q_800)
}
if (band == '850') {
rho_sec <- rho_sec_550 * q_850
rho_sec_err <- rho_sec * (rho_sec_err_550 / rho_sec_550 + q_850_err / q_850)
}
return(list(rho_sec = rho_sec, rho_sec_err = rho_sec_err))
}
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