Signal-to-Noise Ratio in Absorption Imaging

​
optical density of sample
1
readout noise (​
-
e
​)
2.3
dark current (​
-
e
/s)
0.001
clock noise (​
-
e
​)
0
noise factor
1
gain of electron multiplying
1
saturated count rate per pixel ​
-1
μs
​
200
exposure time (μs)
50
plot range of
C
in
10000
This Demonstration analyzes the signal-to-noise ratio (SNR) for a typical absorption image in a cold-atom experiment.

Details

Three components of an absorption image are denoted by:
C
in
(x,y)
, the input light distribution on the atom,
C
out
(x,y)
, the output light (after absorption),
C
bg
(x,y)
, the background.
The formula for calculating the optical density (OD) is
OD(x,y)=
n
col
(x,y)
*
σ
0
=log
C
in
(x,y)-
C
bg
(x,y)
C
out
(x,y)-
C
bg
(x,y)
+
C
in
(x,y)-
C
out
(x,y)
eff
C
sat
,
where
C(x,y)=I(x,y)
A
pix
2
M
λ
hc
TQEτ×
1
ADC
,
I(x,y)
is the intensity distribution of light on the atom,
A
pix
is the pixel size of the camera,
A
pix
2
M
is the real pixel size including the magnification of the image system,
λ
is the wavelength of the probe light,
T
is the transmission rate of the image system,
QE
is the camera quantum efficiency,
ADC
is the analog-to-digital conversion efficiency of the camera,
τ
is the exposure time.
The noise can be written as
2
σ
OD
=
2
∂OD
∂
C
in
2
σ
C
in
+
2
∂OD
∂
C
out
2
σ
C
out
+
2
∂OD
∂
C
bg
2
σ
C
bg
=
2
1
eff
C
sat
+
1
C
in
-
C
bg
2
σ
C
in
+
2
1
eff
C
sat
+
1
C
out
-
C
bg
2
σ
C
out
+
2
1
C
in
-
C
bg
-
1
C
out
-
C
bg
2
σ
C
bg
.
Then, the SNR is
SNR=
log
C
in
-
C
bg
C
out
-
C
bg
+
C
in
-
C
out
eff
C
sat
2
1
eff
C
sat
+
1
C
in
-
C
bg
2
σ
C
in
+
2
1
eff
C
sat
+
1
C
out
-
C
bg
2
σ
C
out
+
2
1
C
in
-
C
bg
-
1
C
out
-
C
bg
2
σ
C
bg
.

References

[1] G. Reinaudi, T. Lahaye, Z. Wang and D. Guéry-Odelin, "Strong Saturation Absorption Imaging of Dense Clouds of Ultracold Atoms," Optics Letters, 32(21), 2007 pp. 3143–3145. doi:10.1364/ol.32.003143.
[2] Thorlabs. "Camera Noise and Temperature Tutorial." (Apr 16, 2021) www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=10773.

Permanent Citation

Zhichao Guo
​
​"Signal-to-Noise Ratio in Absorption Imaging"​
​http://demonstrations.wolfram.com/SignalToNoiseRatioInAbsorptionImaging/​
​Wolfram Demonstrations Project​
​Published: July 8, 2021