Lab1_Final

Testing Gain, Linearity, Dark Current and
Read Noise
In a KAF-0402 Image Sensor
Barbara Pitts RJ Garma
RIT RIT
Bjp4044@rit.edu rdg7649@rit.edu
Abstract—This paper is an examination of tests conducted on a KAF-0402 CCD image
sensor. These tests include gain and read noise calculations, linearity measurements, and
dark current estimation.
Keywords—gain, linearity, dark current, read noise, imaging science, RIT, CCD camera sensors,
image sensors
1 INTRODUCTION AND BACKGROUND THEORY
CCDs are used in a wide variety of cameras and for very different purposes. In order for
these cameras to be used to their full potential, it is helpful to understand the characteristics that
govern a sensor’s performance. This effort is an examination of these characteristics, with
particular interest in gain, read noise, linearity, and dark current.
1.1 Gain and Read Noise
Gain and read noise may be calculated by measuring the mean and standard deviations of
pixel values in two pairs of images with significantly different signal levels, i.e., a pair of bias
and flat-field images. From these images, a rough gain estimate may be calculated using
Gain =
F1 + F2( )− B1 + B2( )
σ 2
F1−F2( ) −σ 2
B1−B2( )
(1)
Where Fn and Bn are the flat and bias frame averages. The denominator contains the standard
deviations of the differenced flat and bias frames. Once gain is calculated, the read noise is
found using
Read Noise =
Gain ×σ B1−B2( )
2
(2)
A more accurate way to simultaneously determine the gain and read noise is by plotting the
variance vs. the mean of multiple flat field images. The variance between each independent
frame expressed as a function of mean signal is
V =
1
G
F +σ R
2 (3)

Where the slope and intercept of a line of best fit from these data will correspond to 1/gain and
the read noise squared, respectively. It is important to note that both methods follow the same
mathematical process, however the latter includes additional data (more than two points),
increasing confidence in the calculated gain value. The specified value for gain and read noise
are 3 e-/ADU and 15 e-, respectively.
1.2 Linearity
CCD linearity is the degree to which the output signal is proportional to the photons
received by the detector. This specification is generally represented as a non-linearity
measurement, i.e., two what extent the data deviates from a line of best fit between a range of
exposure levels. For the sensor used, the manufacturer specification is nominally 1%
(maximally 2%) photoresponse non-linearity (PRNL) between 2% and 90% of saturation. This
measurement is intimately tied to the previous section, as it is essentially a measurement of how
stable the gain remains as a function of signal. In scientific applications, this characteristic plays
an important role if absolute signal levels must be known.
1.3 Dark Current
Dark current is the result of silicone imperfections, the majority of which occur near the
Si and SiO2 interface. Such imperfections provide stepping-stones, i.e., intermediate states, that
allow thermally generated electrons to escape into the conduction band. Such electrons are
indistinguishable from photoelectrons, which imposes added uncertainty when taking
measurements. The most effective way to remove dark current is to cool the CCD, which
precludes electrons from reaching an intermediate state by removing thermal energy.
Empirically, dark current should vary according to
DC = AT 3/2
exp −
Eg
2kT
⎡
⎣⎢
⎤
⎦⎥
(4)
Where is a constant, Eg is the bandgap energy, and T is the detector temperature in Kelvin. For
the KAF-0402ME, the specification of dark current is 15 and 30 e-/pix/s at 25 °C for the nominal
and maximal cases, respectively. The dark current doubling temperature is specified as 6.3 °C.
2 EXPERIMENTAL PROCEDURES
The gain and read noise of the camera were calculated using both techniques outlined in the
previous section. The camera was turned on and allowed to cool for approximately 15 minutes
in order to allow the peltier cooler to achieve a steady-state temperature. This start-up procedure
was used in later data collects. Bias frames were collected using an aperture cover and with the
lights off in order to prevent inadvertent light exposure to the CCD. A uniform field for the flat
frames was generated using the screen of an iPhone 5S in conjunction with a diffuser and two
sheets of paper. The purpose of employing the diffuser and paper was two-fold: to ensure

uniform illumination and to prevent CCD saturation. This configuration is depicted below and
was used for subsequent portions of the lab.
(a) (b)
Figure 1: Camera configuration for collecting flat fields. (a) Diffuser (b) Two sheets of paper.
Flat fields were also collected with the lights off to preclude photon contributions from external
sources. In order to ensure shot-noise limited operation under the given illumination level, a 10 s
exposure time was used when collecting the flat fields for use in Equation (1). Variance and
mean data, used in the second method to calculate gain, were obtained using the schedule
outlined in the table below.
Table 1: Gain and read noise data collection schedule
Exposure Time (s) Frame
25 Frame 1, 2
0 Bias 1 - 5
20 Frame 1, 2
0 Bias 6 - 10
15 Frame 1, 2
0 Bias 11 - 15
9 Frame 1, 2
0 Bias 16 - 20
7 Frame 1, 2
0 Bias 21 - 35
5 Frame 1, 2
0 Bias 26 - 30
4 Frame 1, 2
0 Bias 31 - 35
3 Frame 1, 2
0 Bias 36 - 40
2 Frame 1, 2
0 Bias 41 - 45
1.5 Frame 1, 2
0 Bias 46 – 50
1 Frame 1, 2
0 Bias 51 – 55
0.7 Frame 1, 2
0 Bias 56 – 60
0.4 Frame 1, 2
0 Bias 60 - 100

In order to suppress read noise from the bias image, 100 bias frames were averaged, reducing
read noise from the final bias image by
1
100
=
1
10
Therefore, subtracting this averaged bias from the flat field should preserve read noise in the
final image.
2.2 Linearity
The data used for determining linearity was obtained by exposing the CCD to a uniform field at
different exposure times ranging from 0.2 s to 62 s, which, given the illumination level, was
found to encompass the dynamic range of the camera, accounting for noise sources at the
shortest exposure times. The change in time between exposures ranged from 0.1 and 2 s, the
former being used at the lowest and highest signal levels for the purpose of capturing non-
linearities through increased resolution.
2.3 Dark Current
Dark current was measured at two known temperatures (room temperature and cooled) in order
to determine the dark current and dark current doubling temperature. Room-temperature dark
frames were collected by exposing the CCD in the dark (lights off, aperture cover installed)
according to the schedule in Table 2. In order to record absolute temperature values, warm dark
frames were collected with the top cover removed, allowing direct access to the CCD with the IR
thermometer. Because of noticeable condensation build-up while cooling with the top-cover
removed, cold dark frames were recorded with the top-cover installed. An attempt was made to
calibrate the IR thermometer so that cold temperatures could be derived with the top-cover
mounted, however no predictable, temperature-dependent, patterns were discovered when
measuring CCD temperature with and without the top cover. For this reason, a rough estimate of
the temperature was collected using a single reading after all of the dark data was collected.
Table 2: Dark frame and temperature collection schedule.
Time (min) 5 4 3 2 1
Warm Dark Frame 1 Frame 2 Frame 3 Frame 4 Frame 5
Warm Bias Bias 1, 2 Bias 3, 4 Bias 5, 6 Bias 7, 8 Bias 9, 10
Recorded Temp. (°C) 19.2 18.9 18.9 18.9 19.1
Cool Dark Frame 1 Frame 2 Frame 3 Frame 4 Frame 5
Cold Bias Bias 1, 2 Bias 3, 4 Bias 5, 6 Bias 7, 8 Bias 9, 10
Recorded Temp. (°C) N/A N/A N/A N/A -7.8

3 RESULTS
Uniformity of illumination was verified by scaling a flat field by its median and displaying the
frame, as seen in the figure below. Based on the color bar, it is seen that the frame is fairly
uniform, however center-to-edge non-uniformity exists, which is most likely explained by
aperture vignetting. Avoiding vignetting effects while retaining enough pixels to maintain
statistical significance was achieved by selecting a 100 x 250 pixel subsection for analysis,
indicated by the red box in Figure 2.
Figure 2: Flat fields used in Equation (1). Red rectangle indicates the subsection that was used
for calculations.
Additional detail is seen in Figure 3, which is a scaled plot of the sub-section used.
Figure 3: Sub-section of the flat fields used in Equation (1). It is seen that absolute uniformity
was accomplished to within approximately 2%.
Equations (1) and (2) were used to calculate a gain and read noise of 3.01 e-/ADU and 12.12 e-,
respectively. The second, more accurate, method outlined in Section 1.1 was also used to
calculate these values. The variance and mean were calculated from the data collected in Table
1, and a plot is seen in the figure below.

Figure 4: Variance vs. Mean Plot
Both sets of results are summarized in the table below.
Table 3: Mean, Standard deviation, Read Noise and Gain.
mean
(ADU's)
STDV(f1-‐f2)^2

Flat
1
18002.33
9848.1

Flat
2
21798.73

For read noise
mean
(ADU's)
STDV(b1-‐b2)^2
STDV(b1-‐b2)

Bias
1
3196.38
32.37
5.69

Bias
2
3202.52

Gain
Read
noise

Method 1 (e-/ADU) 3.01
12.12

Method 2 (e-) 12.12
-15

The gain calculated by both methods are close to what is expected for this camera, given a full
well depth of 100,000 e- and an dynamic range of 15 bits. For Method 1, a calculated read noise
of 12.12 e- is reasonable given a manufacturer specification of 15 e-. The read noise calculated
by using the intercept of the plot is problematic because it is negative. Re-calculating the read
noise using the gain from Method 2 and Equation (2) produces a value of 13.8 e-, much closer to
specification. The lower-than expected read noise may be a result of higher signal data skewing
the plot to have a lower intercept value.
3.2 Linearity
As seen from the figure below, the CCD is found to be highly linear. The data exhibits
instability toward the upper and lower limits of the plot, which may be attributed to short
incremental increases/decreases in exposure time (0.2 s) and limitations in shutter accuracy. It
can also be seen that the signal reaches a plateau indicating saturation. Using the saturation point

as the maximum value, data points lower than 2% and higher than 90% were eliminated, seen in
Figure 5b.
(a) (b)
Figure 5: Linearity Plots. (a) Full range of data (b) Between 2% and 90% of full well. Error bars are the
red markers.
A line of best fit was calculated from this subset, resulting in an R2
of 0.99. From Figure 5b, it
can also be seen that the data falls between the +/-2% plot lines, indicating that the CCD meets
manufacturer specification.
3.3 Dark Current
Using the data collected in Table 2, a plot of mean electron count vs. time was generated and is
seen in Figure 6. The average room temperature was calculated to be 19 °C, while the cooled
temperature estimate recorded after collecting data was -7.8 °C.
Figure 6: Dark current plot

Error bars were calculated using a confidence level of 95%. Calculating the slope of each line
results in a dark current of 6.77 and 0.4 e-/pix/s for the warm and cool cases respectively. Using
the nominal specification of 15 e-/pix/s at 25 °C and a dark current doubling temperature of 6.3
°C, the theoretical dark current at 19 °C is calculated to be approximately 7.5 e-/pix/s, a close
match to our measurements. Similarly, theoretical dark current at -7.8 °C is calculated to be 0.4
e-/pix/s, also consistent with our results. These are summarized in the table below.
Table 4: Dark Current based on measurements and calculated
values using measured temperature and manufacturer specification
Measured Specification
Warm Dark Current (e-/pix/s) 6.77 7.5
Cool Dark Current (e-/pix/s) 0.4 0.4
4 CONCLUSIONS
The gain, read noise, linearity, and dark current of the sensor were investigated and characterized
for this lab. Some of the difficulties included capturing a flat field, ensuring the camera’s
temperature was stable, and determining the absolute temperature of the CCD. Data sets were
taken multiple times as laboratory procedures were fined-tuned to eliminate discrepancies and
unwanted variance in the data.
Both methods for calculating gain yielded similar results that agreed with the manufacturer
specification; however read noise calculations varied widely. The first method for calculating
read-noise resulted with a value that was close to the specification. Using the variance and mean
technique produced a read-noise much lower than expected, which may have been attributed to
the higher signal levels increasing the slope of the variance plot.
From the linearity data it can be seen that the CCD is very stable between the ranges specified by
the manufacturer. Near full well, it was seen that the slope tapered and eventually plateaued,
which is consistent with expectations. At low signal levels, the noise floor of the camera is
reached resulting, also resulting in a signal plateau.
Dark current calculations produced results similar to the calculated the manufacturer
specification. The dark current recorded at room temperature was lower than the specification,
but this discrepancy may be due to the very cold conditions experienced in the lab during that
collection. Dark current measured while cooling the CCD matched calculations using recorded
temperature and manufacturer specifications for nominal dark current and dark current doubling
temperature.

REFERENCES
"Measuring CCD Read Noise." Measuring CCD Read Noise. N.p., n.d. Web. 24 Feb. 2014.
http://qsimaging.com/
Photometrics. (2014, Feb 15th). Imaging Learning Zone. [Online]. Available:
http://www.photometrics.com/resources/learningzone/darkcurrent.php

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