SCULIB_J_THEORETICAL

calculate the theoretical sky brightness temperature

This routine calculates the theoretical sky brightness temperature according to Bill Duncan’s model:-

J_{}

meas = (1 -

η_{}

tel) J_tel + $η_{}$

tel J_atm - b $η_{}$

tel J_atm e^-A $τ, (52)$

Jtel is known and Jatm is related to Jamb by:-

J_{}

atm = J_amb

\int_{0}^{40} A [k exp (- \frac{h}{h_{2}}) exp [A k h_{2} (exp (- \frac{h}{h_{2}}) - 1)] (1 - \frac{h}{h_{1}})] d h, (53)

where h2 = scale height of absorption ( = 2km), h1 = coefficient to give 6.5K/km temperature drop in absorber, A = airmass, k = extinction.

which relation has been fudged by Bill Duncan to:-

J_{}

atm = J_amb X_g

[1 - exp (- A k h_{2})], (54)

with

X_{}

g $h a v i n g t h e f o r m$

g = 1 + h_2 T_lapse $T_{}$

amb $e x p (- \frac{A τ}{X_{}})$

gconst $(55)$ with

h1 = 2, h2 = -6.5 (note this h2 is defined differently to that in the previous equation), $X_{}$

gconst $= 3.669383$

where Jatm is the effective brightness temperature of the sky.

The routine will return immediately if entered with bad status. Errors will be reported and bad status returned if:-

CALL SCULIB_J_THEORETICAL (TAUZ, AIRMASS, T_TEL, T_AMB, WAVELENGTH, ETA_TEL, B, J_THEORETICAL, STATUS)

zenith sky optical depth

airmass

temperature of the telescope (K)

temperature of ambient air (K)

wavelength of interest (microns)

telescope transmission

bandwidth factor

the theoretical sky brightness temperature

global status