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Next: F.2 Greek Symbols Up: F. List of Symbols Previous: F. List of Symbols


F.1 Roman Symbols

Symbol   Explanation
$A$   area
$A$ area of primary mirror
$A(a)$ area of aperture $a$
$a$ aperture
$A$ generic constant
$A_{0}(t_{1},t_{2})$ offset of linear regression in the reset interval correction
$A_{1}(t_{1},t_{2})$ slope of linear regression in the reset interval correction
$A_{0}$, $A_{1}$ first order correction on point source spectral response function
$A_{0}$, $A_{1}$ first order signal corrections for PHT-S chopped observations
$A_{0}(i)$, $A_{1}(i)$ coefficients for signal dependent PHT-S correction
$a(SED)$ flux density conversion factor
$A_{chop}$ empirical asymmetry factor for chopper offset
$A_0,A_1,A_2,A_3,A_4,A_5$ coefficients for chopper offset correction
$B$ surface brightness
$B(i,j)$ mean brightness
$B_{back}$ background surface brightness
$B_{n}(i,j)$ accumulated sum of first n sky measurements to
mean brightness
$B$ generic constant
$c_{light}$ speed of light $c$= 299792500 ms$^{-1}$ in OLP
$c$ generic constant
$C$ generic constant
$C_{1}$, $C_{2}$ constants
$C(*)$ statistic
$C_{int}$ detector capacitance
$C^{det}_{int}$ idem for detector $det$
C1$^{f}$ constant for transmission of the whole optical path for a given filter
assuming $\nu f_{\nu}=const$ as reference spectrum.The effective size
of the primary mirror; reflection losses, filter transmission, spectral
response of the detector, etc. are included
$C(i)$ spectral response function for pixel i
$C^{c,p}_{avg}(i)$ average spectral response function for a point source
$C^{c,p}(i)$ spectral response of pixel i for a point source p corrected for chopped c
signal losses
$C^{c,s}_{avg}(i)$ average spectral response function for PHT-S staring observations
$C^{c,p}(i)$ spectral response function for pixel i corrected for chopped signal loss
$C^{c,p}_{ave}(i)$ PHT-S averaged chopped spectral response function for a point source
$C^{det}_{int}$ integration capacitance associated with detector P1, P2 or P3,
$C_{phts,pixel}$ point source responsivity for PHT-S pixel
$C^{E}_{phts,pixel}$ extended source responsivity for PHT-S pixel
$d$ height of source peak (background subtracted)
$d_{airy}$ diameter of Airy disk
$D_{A}$ diameter of aperture for PHT-P, side length of the array for PHT-C
Dec declination
DI selected offset data word (0...4095)
$D_{0}$ fixed voltage offset for CRE
$e$ exposure time
e$_{n}$(i,j) contribution from nth sky sample to exposure time
$E$ accumulated exposure time
$E_{n}$(i,j) sum of first n sky pointings
$E_{total}$(i,j) total exposure time of image
$f$ filter
$f_{\nu}$ flux density
$f^{f}_{PSF}$ point spread function fraction for filter f
entering the field aperture in case of PHT-P or falling onto the
array in case of PHT-C
$f_{PSF}$ intensity function of a point source entering the aperture
$f_{PSF}(\lambda_{c}, aperture)$ fraction of the telescope point spread function falling into a given
aperture for PHT-P or onto the full array for PHT-C
$f^{aperture}_{psf}$ idem for a given aperture
$f^{array}_{psf}$ idem for the entire detector array
$f^{pixel}_{psf}$ idem for a given pixel
$f_{psf}(\lambda_{ref})$ fraction of point spread function at the reference wavelength $\lambda_{ref}$
$f_{beam}(\lambda)$ wavelength dependent beam profile
inside the aperture or pixel
$f_{cov}$ coverage factor
${\char'13}(i)$ flat-field correction for pixel $i$
$F$ flux density in frequency units unless explicitly specified
$F_{\nu}$(i,k) flux for pixel i at raster point k
$F_{scr+back}$ source+background flux
$F_{on}$ source+background flux
$F_{back}$ background flux
$F_{off}$ background flux
$F_{scr} $ source flux with psf correction for point source
$F_{\lambda}$(i) flux density in wavelength units for pixel $i$
$F(\lambda)$ flux density of source at specific wavelength $\lambda$
$F^{f}_{\nu}$ source flux density for an assumed spectral energy distribution
$\nu f_{\nu}=const$
(flux density at reference wavelength)
$F_{\nu}(\lambda_{c})$ flux density at centre wavelength of filter
$F_{\nu_{ref}}(SED)$ flux density for applied SED
$F_{\nu_{ref}}(\nu^{-1})$ flux density quoted in AAR
$F(\nu)$ flux density in frequency range
$F(\lambda)$ flux density in wavelength range
$F^{f}_{\nu}$ source flux density for an assumed spectral energy distribution
$\nu f_{\nu}=const$ at reference wavelength
$g(i,S(i,t),t)$ weighting function for correction $\phi$
$g(i,S,t)$ weight factors related to correction $\varphi$(i,S,t)
$g_{fit}$ goodness of fit
$G$ gain
$G_{off}$ offset gain
$G_{signal}$ signal gain
$h$ Planck constant
$h$ heating power of FCS
$H(S)$ linearisation correction for signal S
$H^{f,i}(s)$ idem, for filter $f$, detector pixel $i$, and signal $s$
$i$ pixel index, integer counter
$I$ Surface brightness in wavelength units unless explicitly stated
$I_{\nu}(\lambda_{c})$ surface brightness based on monochromatic point source flux density
$I^{f}_{\nu}$ surface brightness of (extended) source in filter f, assuming
$\nu F_{\nu}=const$
$I_{\lambda}$(i) surface brightness of a given detector array element i (of PHT-S)
IBP in-band power in W
$I_{step}$ step flag, for chopper position within a chopper cycle
$k$ integer counter
$k$ chopper cycle number
$k$ raster point number in one direction
$k$ Boltzmann's constant
$k_{f}$ colour correction
$K$ constant
$K_{CC}$(SED) colour correction factors for applied SED
$l$ length or integer counter
$l$ raster point number in one direction
$L$ length
$L_{\alpha}$ map size in RA
$L_{\delta}$ map size in Dec
$m_{pix}$ mean pixel value used to convert into the correct units
$M$ number of raster steps along a raster leg
$m(u)$ median of s$_{diff}$ per chopper unit
$M$ number of columns of raster
n integer counter
n$_{\alpha}$ minimum number of image pixels in RA to cover raster area
n$_{\delta}$ minimum number of image pixels in Dec to cover raster area
n$_{d}$ index representing the dwell time in the calibration files
n$_{pix}$ number of detector pixels
N integer counter
$N_{it}$ number of iterations for ramp deglitching
$N_{min}$ minimum number of readouts per ramp
$N_{\sigma}$ sigma value to identify outliers in ramp deglitching
$N_{u}$ number of chopper units
$N_{r}$ number of ramps per chopper plateau
$N_{read}$ total number of readouts
$N'_{r}$ actual number of ramps per chopper plateau in the telemetry, is derived
from N'$_{r}$ = N$_{r}$/DAT_RED where N$_{r}$ is the commanded number of
ramps per chopper plateau and DAT_RED is the applied data reduction
factor
$N_{fg}$ number of fine grid positions that fall within the detector footprint
$N_{total}$ total number of fine grid positions that fall within a pixel
$N_{cc}$ cirrus confusion noise
$N_{gc}$ galaxy confusion noise
$P$ power in W
$P^{f'}_{fcs}(h)$ in-band power for filter f' and FCS heating power h in mW as obtained from
FCS power tables, for PHT-P in Wmm$^{-2}$,
for PHT-C in W/pixel
$P_{src}$ source power
$P_{C}$ power measured on pixel if line is centred
$P^{1}_{C}$ power measured on adjacent pixel if line is centred
$P_{M}$ power measured on pixel if line is centred between pixels
$P^{f}_{fcs}$(h) in-band power for filter f and FCS heating power h
$P^{f}_{cal}$ in-band power of celestial calibrator
$P^{f}_{scr}(a)$ in-band power for filter f in aperture a
$P^{f}_{scr}(i)$ in-band power for filter f and pixel $i$
$P_{max}$ maximum commandable power on FCS
$P(s+b)$ in-band power of on-source position
$P(b)$ in-band power of off-source position
$P(s)$ in-band power of source only
$P_{gauss}(s)$ peak (source) power value
$P_{gauss}(b)$ background power value
$P_{fcs}(f,h)$ in-band power on the detector from the FCS due to heating power h
$P_{target}(f')$ in-band power obtained from the source
$P_{fcs}(f,h)$ in-band power for given FCS heating power h
$P$ constant
$q$ detection limit in multiples of $\sigma$
$Q$ quaternion
$Q_{raster}$ quarternion that defines the position of the PHT central field of view for
a given raster point in the J2000 inertial frame
$Q_{str}$ defines the J2000 pointing of the ISO star tracker
$Q_{r}$ defines the raster point relative to the raster centre of the scan
$Q_{str/qss}$ describes misalignment between the star tracker and the quadrant star
sensor (QSS)
$Q_{qss/pht}$ describes the QSS to instrument aperture alignment
$Q_{cor}$ gives the fine pointing correction to the star tracker calibration
$Q1, Q2$ quarternions representing the rotations of the detector origin with
respect to a given raster point, assuming perfect alignment between
chopper and spacecraft y-axis
$Q_{chop}$ chopper quaternion
$Q$ constant
$R$ responsivity
$R_{c}$ average relative system response derived from a bandpass
$R_{det}$ detector responsivity
$R_{det}$(i) detector responsivity of pixel i
$R_{default}$ default detector responsivity
$R(i)$ responsivity for each pixel of a C detector
$R_{FCS}(i)$ responsivity of pixel $i$ obtained from FCS
$R(\lambda)$ system response at specific wavelength
$R_{s}$ sensor resistance
$R$ constant in resistance
$R_{k}$ harness resistance
$R_{p}$ EEU shunt resistor in parallel to sensor
$r(i)$ measured responsivity of pixel $i$ relative to default responsivity
$s$ signal in V/s
$s_{src}$ source signal
$s(t)$ signal at time t
$s(k)$ pairwise differences between V(k) and V(k+1)
$s(j)$ slope for ramp j
$s(RI, DAT\_RED)$ signal taken with reset interval RI and data reduction rate DAT_RED
$s'(\phi(t))$ signal after orbital dependent dark correction
$s(\phi(t))$ initial signal
$s_{dark}$($\phi$(t)) orbit dependent dark correction
$s_{old}$ signal before signal linearisation
$s_{new}$ signal after signal linearisation
$s(k)$ signal
$<s>$ average of valid signals per chopper plateau
$s_{diff}$ difference signals of consecutive readouts
$s(i)$ generic pattern
$s_{scr}$ source signal determined via generic pattern
$s^{c}_{scr}$ source signal determined via generic pattern, corrected for losses due to
chopper modulation
$s_{k}$(x) source signal for chopper cycle k
$s_{k}$(X) given set of powers
$<s_{fcs}(f)>$ weighted mean signal for FCS measurement
$<s_{fcs}(i,f)>$ FCS signal per chopper plateau
$s_{pixel}$ image pixel size
$s$ nominal uncertainty of fit
$s'$ uncertainty of fit
$S$ signal
$S_{src}$ linearised difference signal (from chopped measurement)
$S'_{src}$ linearised difference signal, corrected for losses due to chopper
modulations
$S_{on}$, S$_{off}$ on- and off-source signals
$S(i,k)$ signal for pixel i at raster point k
$S^{f}_{cal}$ measured signal of calibrator
$S^{f}_{str}$ measured dark FCS signal (stray light)
$S^{f'}_{fcs}$ signal of FCS measurement in filter f'
$S_{scr}(a)$ linearised source signal (PHT-P) after dark signal subtraction
$S_{scr}(i)$ linearised source signal (PHT-C) after dark signal subtraction
$S(i,t)$ signal transient of pixel i at time t
$S^{det}_{dark}$ orbit dependent dark signals
$S$ size
$S_{fine grid}$ side length of (square) fine grid image pixel
$S_{pixel}$ side length of square detector pixel
$t$ time in s
$t_{mid}$ time at midpoint of a given ramp
$t_{0}$ time at first readout of a given ramp
$t_{dwell}$ chopper dwell time
$t_{m}$ measurement time
$t_{r}$ reset interval time
$t_{plat}$ chopper plateau time
$t_{n}$ dwell time
$T$ temperature in K
$T$ EEU temperature
$T_{refl}$ reflection losses on optical elements
tmd telemetry data value
$tmd_{max}$ maximum value of telemetry word (=4096)
TOL voltage for chopper deflection calibration
RA right ascension
$u$ chopper unit
$u$ uncertainty
$u_{n}$(i,j) mean brightness uncertainty contribution from nth sky sample
$U$ voltage in V
$U_{ACF_{1}}$ voltage for chopper deflection calibration
$U_{DCF_{1}}$ voltage for chopper deflection calibration
$U_{OF_{1}}$ voltage for chopper deflection calibration
$U_{OF_{2}}$ voltage for chopper deflection calibration
$U_{CRE}$ CRE output voltage
$U_{off}$ GAIN$_{1}$ dependent offset voltage
$U$ uncertainty
$U_{n}$(i,j) accumulated mean brightness uncertainty
$U_{rms}$(i,j) brightness uncertainty from rms
$V$ voltage in V
$V(k)$ voltage corresponding to readout k
$V_{ini}$ voltage
$w$ weight
$w(i,t)$ weight function for PHT-S chopped measurements
$w_{j}$ statistical weight of each signal obtained from its associated statistical
uncertainty
$x$ distance or coordinate
$x_{m}$ margin around raster in m direction
$x_{n}$ margin around raster in n direction
$x_{0}$ angular x coordinate of the image pixel origin
$X^{raw}_{FPC}$ data word for focal plane chopper position
$y$ distance or coordinate
$y_{det}$ chopper deflection
$y_{0}$ angular y coordinate of the image pixel origin
$z$ distance or coordinate
$z_{det}$ spacecraft z-offset


next up previous contents index
Next: F.2 Greek Symbols Up: F. List of Symbols Previous: F. List of Symbols
ISO Handbook Volume IV (PHT), Version 2.0.1, SAI/1999-069/Dc