On Friday, I tried calibrating the CCD with the following setup. Here, I present the expected values of scattered power (Ps) at  s = 45°, where s is scattering angle (refer figure). The LED box has a hole with an aperture of 5mm and the LED is placed at approximately 7mm from the hole. Thus the aperture angle is 2*tan-1(2.5/7) ≈ 40° approx. Using this, the spot size of the LED light at a distance 'd' was estimated. The width of the LED holder/stand (approx 4") puts a constraint on the lowest possible s. At this lowest possible s, the distance of CCD/Ophir from the screen is given by  . This was taken as the imaging distance for other angles also.
In the table below, Pi is taken to be 1.5mW, and Ps and  were calculated using the following equations:
 
|
d (cm)
|
Estimated spot diameter (cm) |
Lowest possible s (in degrees)
|
Distance of CCD/Ophir from the screen (in cm) |
(in sr) |
Expected Ps at s = 45° (in µW)
|
| 1.0 |
1.2 |
78.86 |
5.2 |
0.1036 |
34.98 |
| 2.0 |
2.0 |
68.51 |
5.5 |
0.0259 |
8.74 |
| 3.0 |
2.7 |
59.44 |
5.9 |
0.0115 |
3.88 |
| 4.0 |
3.4 |
51.78 |
6.5 |
0.0065 |
2.19 |
| 5.0 |
4.1 |
45.45 |
7.1 |
0.0041 |
1.38 |
| 6.0 |
4.9 |
40.25 |
7.9 |
0.0029 |
0.98 |
| 7.0 |
5.6 |
35.97 |
8.6 |
0.0021 |
0.71 |
| 8.0 |
6.3 |
32.42 |
9.5 |
0.0016 |
0.54 |
| 9.0 |
7.1 |
29.44 |
10.3 |
0.0013 |
0.44 |
| 10.0 |
7.8 |
26.93 |
11.2 |
0.0010 |
0.34 |
On measuring the scattered power (Ps) using the ophir power meter, I got values of the same order as that of expected values given the above table. Like Gautam suggested, we could use a photodiode to detect the scattered power as it will offer us better precision or we could calibrate the power meter using the method mentioned in Johannes's post: https://nodus.ligo.caltech.edu:8081/40m/13391.
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