Signal to noise ratio/CCD saturation problem

[s_gunn]

Homework Statement

A 4m telescope has a 16bit controllr with a gain of 1 and must detect faint stars(M>15) without saturating the bright stars(M=8-10).

(i) What is the max no of photo-electrons that can be registered before saturating the CCD?

(ii) The zero point of the system is 16.5mag, what is the longest exposure of a mag 8 star without saturation? (all counts fall on 1 pixel)

(iii) The CCD has read noise of 4 and no dark current. If the SNR is 5 and the background count is 0.1 per second, what is the magnitude of the faintest star that can be detected?

(iv) If the controller is updated to 22bit, what exposure can be used before saturation?

(v) What mag will be the faintest in this case?

Homework Equations

(ii) [tex]m_{zp}-m_{std}=-2.5log(\frac{1 count/sec}{f_{std}})[/tex]

(iii) [tex]SNR=\frac{Signal}{\sqrt{signal+Background+Dark+Read^{2}}}[/tex]

The Attempt at a Solution

(i) total photo electrons = 2^16 = 65536

(ii) (using equation (ii)) 26.09sec

(iii) (using Equation (iii)) m=16.108

(iv) (using equation (ii)) 1669.71sec

(v) (using equation (iii)) m=20.6


I just wanted to check if I've gone about this the right way if anyone would like something to work through!

 

[Jhero]

Yes, your approach and calculations seem correct. However, there are a few things that you could clarify or expand on to make your answer more thorough:

(i) It would be helpful to include the equation for calculating the maximum number of photo-electrons that can be registered before saturation. Also, specify the units of measurement (e.g. electrons, counts, etc.).

(ii) Your calculation for the longest exposure time is correct, but you could also explain the significance of the zero point and how it relates to the maximum exposure time for a bright star before saturation.

(iii) In addition to the equation for SNR, you could also mention the assumptions made in this calculation (e.g. Gaussian noise, no systematic errors, etc.). Also, clarify the units of measurement for the background count and the read noise.

(iv) Similarly to (i), it would be helpful to include the equation for calculating the maximum exposure time before saturation with a 22-bit controller.

(v) You could also mention the significance of the faintest magnitude for detecting faint stars and how it relates to the capabilities of the telescope and controller.

Overall, your solution is correct and well-organized. Including some additional explanations and clarifications would make it even more comprehensive. Keep up the good work!