Signal to Noise Ratio Calculation

According to : Detecting and measuring faint point sources with a CCD (Herbert Raab)

 

 

Telescope data

1

Mirror diameter

0.305 m

D

2

Obstruction

0.10 m

O

3

Ligth collecting area

0.063 m2

(p . D2 - p . O2)/4

4

Focal ratio

4

 

5

Focal lenght

1.22 m

 

 

Detector (MX716)

6

Pixel size

17.2 mm

Binning 2x2

7

Pxel scale

2.7 /pixel

 

8

Dark current

0.1 e-/s/pixel

 

9

Readout noise

12 e-/pixel

 

10

Quantum efficiency

65%

 

11

Integration time

100 s

600 s

T

12

FWHM

4

 

Object and Sky

13

Object magnitude

19

20

 

14

Object flux

6927 g

16625 g

4 . 1010/2.5m g/sec/m2

. t sec . 0.063 m2

15

Object signal

4502 e-

10806 e-

(14)*(10)

16

Share for central pixel

.29

.29

Function of FWHM

17

Object signal in central pixel

1306 e-

3134 e-

(15)*(16)

18

Object Noise in central pixel

36 e-

56 e-

SQRT(17)

19

Sky background

18 mag/^2

18 mag/^2

Brightness per squared arc second

20

Sky back. Flux

126243 g/pixel

757459 g/pixel

4 .1010/2.5m g/sec/ m2/ 2

. (11) . (3). (7)2

21

Sky back. signal

82058 e-/pixel

429348 e-/pixel

Flux . quantum efficiency

22

Sky back. noise

286 e-/pixel

702 e-/pixel

 

23

Dark current

10 e-/pixel

60 e-/pixel

 

24

Dark noise

3.2 e-

7.7 e-

 

25

Noise in central pixel

288 e-

704 e-

SQRT((18)2+(22)2+(24)2+(9)2)

26

Peak SNR

4.55

4.45

(17)/(25)