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PHYS 3041 Research Topic in Physics: Write Up 74" Telescope Efficiency Response
by Philip Lah Supervisor: Paul Francis Date: 1st Semester 2002

Hubble Telescope Image of Eta Carinae Discussion

74" Telescope Image of Eta Carinae

The goal of this Research Project is to determine what percentage of the light from an object is actually detected by the 74" Mt Stromlo telescope at different wavelengths. This information will be used to determine the exposure time required for an object of a given magnitude to get a good signal to noise ratio. The 74" Mt Stromlo telescope was constructed in the 1950s and has a mirror diameter of 74" (1.9 m) with a mirror collecting area of 2.483 m2. Standard stars, whose luminosity at all relevant visible wavelengths are known, were selected from the paper "Spectrophotometry: Revised Standards and Techniques" by Michael S. Bessel. These were observed with the 74" telescope in as clear as was possible conditions using a Cassegrain Spectrograph mounted on the telescope linked to a liquid nitrogen cooled digital CCD (Charge Coupled Device). From the known luminosity of the standard star the number of photons from the star that hit the atmosphere at each wavelength was calculated using n = f = f `n' the
hМ hc

number of photons and `f' the known flux at a particular wavelength. This number was then compared with the number of photons detected by the telescope as electrons to determine the efficiency of the telescope at each wavelength. There are a number of sources of loss that stops one from detecting 100% of the incident photons. The best one can currently do with the world's best equipment is about 40% efficiency but the efficiency of the 74" telescope is well below that. There are many sources of loss with the main ones listed here. There are losses in the atmosphere as water droplets in clouds scatter light. Of particular importance to our observations were Cirrus clouds (high formation of clouds in wispy filaments) that were around during some of our observing. Not all the light from the object goes 1


down the narrow slit of the spectrograph. Also only the 1st order diffraction peaks from the spectrographs diffraction grating were measured so any light in the 2nd order or higher orders is not detected. The grating's response is only maximised for one wavelength around 500 nm (green) so that the further the light is away from this value the more light is lost. There are also losses at the various lenses and mirrors that focus the light in the detection system and the CCD does not pick up every photon incident on it. Besides the losses in the telescope system there are also sources of noise that add to the signal. The first one is noise from the sky. This noise consists of the lights of Canberra, any moon that is up at the time of observation and the general glow of the atmosphere. The sky noise was measured at various wavelengths by taking a spectrum away from any bright objects. The sky noise can be subtracted from an object by measuring the surrounding sky and extrapolating under the object. This can be done very accurately so that it is possible to observe objects that are much fainter than the sky noise. Another source of noise is the n Poisson Noise from quantum mechanical effects. The uncertainty principle adds noise as the incoming photons have a position that is restricted due to the fact that it must pass through the telescope, the optics and land on a tiny pixel. This fixing of the photons position creates an uncertainty in the light's energy that is seen as noise. Another source of noise occurs when the number of electrons detected is converted from its original analogue voltage to a digital signal, which is not a perfect conversion. There is also the Read Noise of the electric equipment that is there even when there is no light entering the telescope. This was measured by taking two zero time exposures with the telescope and subtracting them from each other. This subtraction removes any fixed pattern, in this case upward stripes near the edges. The fixed pattern is easily calibrated for so it can be ignored. The subtraction leaves behind any random noise that makes up the Read Noise. The subtraction leaves you with 2 times the read noise, which was calculated in this case to be 8.512 electrons per pixel. There may also be sensitivity differences from pixel-to-pixel in the CCD. Using a quartz lamp of known luminosity and measuring the CCD's response for each pixel one can calibrate these differences out. The CCD used was actually fairly uniform so that this step was not necessary. To calibrate the wavelength of the telescope-spectrograph system an Argon Ion lamp with known spectral lines was used. The width of a spectral line in the Argon spectrum was used to determine the width of the CCD's resolution element, which was found to be 2 pixels wide. This gives a resolution of about 0.5 nm. The resolution of the spectra is limited by the equipment rather than object that is observed. The length of a resolution element was found to be 10 pixels by looking at an image of an actual object. This value depends on the seeing. That gives us a total of 20 pixels per resolution element. The gain, the conversion from ADU to electrons detected by the CCD, was determined to be 2.33 e /ADU. The gain is used to calculate how many photons are detected per resolution element with each photon detected corresponding to one electron measured.

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Results The efficiency of the 74" telescope, that is the ratio of electrons detected to the photons incident on the telescope ignoring atmospheric effects, is listed in the below table. This was calculated from the known flux of the standard stars. Band B V R Wavelength 440 nm 550 nm 700 nm Efficiency 2.8% 4.3% 2.9%

The magnitude for which the sky's brightness equals the object's brightness is listed in the below table. For object magnitudes greater than this magnitude the major source of signal is from the sky. There was no moon up during the observing run. Sky Limited for m greater than 17th magnitude 16th magnitude 16th magnitude

Band B V R

Wavelength 440 nm 550 nm 700 nm

The formula for the signal to noise ratio is given below for each of the three visible light bands. It is a function of magnitude of the object `m' and the exposure time `t'. For B Band

Signal = Noise

Counts

(Poisson_Noise)

2

+ (Read_Noise)

2

=

4.9 в 106 2.5112m + 1.1 в t 4.9 в 106 + 1.1 в t + 1444 2.5112m

For V Band

Signal = Noise

Counts

(Poisson_Noise)2 + (Read_Noise)2
5.2 в 106 2.5112 m + 1.5 5.2 в 10 6 + 1.5 в m 2.5112 вt t + 1444

=



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For R Band

Signal = Noise

Counts

(Poisson_Noise)2 + (Read_Noise)2
2.8 в 10 6 + 1.2 в t 2.5112 m 6 2.8 в 10 + 1.2 в t + 1444 m 2.5112

=



For faint sources (m large) the sky noise will dominate. It is then required that the Poisson Noise be greater than the Read Noise to get a reasonable signal. In the below table are the required exposure times for which Poisson Noise is greater than the Read Noise as magnitude goes to infinity (object luminosity goes to zero). Exposure Time for Poisson Noise greater than Read Noise 22 minutes (1300 s) 16 minutes (960 s) 20 minutes (1200 s)

Band B V R

Wavelength 440 nm 550 nm 700 nm

Below are tables of the exposure time required in each band to get a signal to noise ratio of 10 at a given magnitude. for B Band For Signal to Noise Ratio of 10 Magnitude Exposure Time Required 12 5.4 s 14 31 s 16 140 s 18 300 s for V band For Signal to Noise Ratio of 10 Magnitude Exposure Time Required 12 5.0 s 14 29 s 16 120 s 18 230 s for R band For Signal to Noise Ratio of 10 Magnitude Exposure Time Required 12 9.3 s 14 51 s 16 183 s 18 310 s 4


Calculations in detail for B Band 6.32 в 10 -11 f= Wm - 2 nm m 2.5112
-1

f=Flux above atmosphere, m=magnitude of object

hc , К=440 nm, over the collecting area of mirror A=2.483 m2 and for each resolution element R=0.5 nm. This is converted to a photon flux at particular wavelength E =

n=

fAR 6.32в10-11 в 2.483в 440в10-9 в 0.5 1.7 в108 -1 -1 = = s res hc 2.5112m в 6.62в10-34 в 3в108 2.5112m

n=number of photons per second per resolution element hitting the mirror ignoring the effect of the atmosphere The efficiency at the B band (440 nm) was 2.8% from the data. Therefore:

4.9 в106 -1 ne = s res 2.5112m
second

-1

ne=number of electrons detected per resolution element per

Sky Brightness= 0.023 ADU s-1 pixels-1 from data. Number of electrons=sky в gain в number of pixels per resolution element. nsky =0.023в2.33в20=1.1 e- s-1 Object brightness less than brightness of the sky: (means that sky noise will be the dominant noise source).

object < sky 4.9 в 10 6 < 1.1 2.5112 m m > 17
Therefore sky limited in B band for m>17th magnitude Counts=number of counts, t=exposure time

4.9 в106 Counts= (object+ sky) в t = 2.5112m + 1.1 в t in Counts per second
PN=Poisson Noise

4.9 в 10 6 PN = Counts = 2.5112m + 1.1 в t in Counts per second
RN= read Noise per pixel; P=number of pixel per resolution element Read Noise = RN в P = 8.512в 20 = 38 Count s -1

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Signal = Noise

Counts

(Poisson_Noise)2 + (Read_Noise)
4.9 в 106 + 1.1 в t 2.5112m 4.9 в 106 2.5112m + 1.1 в t + 1444

2

=

For a faint source (`m' approaching infinity) sky noise will dominant so require Poisson Noise greater than Read Noise in this case. Poisson Noise> Read Noise
1.1t > 38 t > 1300 s = 22 min

An exposure time of 22 minutes is required to get a signal above the Read Noise. The calculation of the exposure time required for a Signal to Noise Ratio of 10 is given below: Counts= (object+ sky) в t = a(m)в t a(m)=(object+sky)
Signal = Noise 10 = Counts

(Poisson_Noise)
a(m) в t a(m) в t + 1444

2

+ (Read_Noise)

2

solving for t 425 a(m) for B band t=

4.9в106 a(m) = + 1.1 2.5112m
Note: All of the above calculations for V and R bands are similar to that for the B band so that they are not listed here only their results above.

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