Here is how noise sources can be either eliminated or made insignificant in CMOS image sensor designs.
The part 4 of this article series looked at the operation of the 3T and 5T charge-transfer pixels in some detail. The characteristics of the pixel were examined during reset and charge integration. We saw how the rolling shutter functions, why the start and stop times of each line are time-offset, and how the reset reference used for a given exposure is a measurement of the reset level for the next exposure versus the one at hand. We also saw how the reset voltage level can be affected by prior exposure, leading to image lag, and how altering the operating voltage for the reset control can improve the situation.
Next, the article showed how the basic 5T charge-transfer pixel can resolve the reset reference level issue by using a method to separate charge integration from charge sensing functions in the pixel. Finally, we saw that the charge-transfer pixel can operate in both rolling shutter and global snap shutter modes, leading to a way to solve the focal plane distortion problem suffered by the rolling shutter operating mode when motion is present in the scene. We also noted that the dynamic charge storage used in the charge-transfer pixel can result in degraded images caused by increased noise due to dark signal.
This article will look at the basics of noise in digital camera designs.
The basis for creating an electronic image from a CMOS image sensor is the photoelectric effect, discovered by Einstein and the subject of his 1921 Nobel Prize in physics. Photons of sufficient energy interact with silicon creating hole-electron pairs, which are charged particles. Because they are charged, h-e pairs can be manipulated, moved and collected by electric fields, so they can be measured as part of making an electronic image.
Photons follow Poisson statistics: there will be an average number of photons collected during any given period of time, but the actual number will vary due to the discrete nature of the source. It’s the source of photon shot noise, leading to measurement uncertainty that arises from the discrete nature of photons.
From a numerical perspective, this shot noise is equal to the square root of the number of photons interacting with the silicon. For the visible light range, each interacting photon creates a single h-e pair. Therefore, the shot noise for an electron-operated visible light device is:
shot noise (e-) = SQRT (signal(e-))
The shot noise is the minimum possible noise in a single electronic image; it represents the noise floor.
If shot noise versus signal is plotted on log-log axes, a straight-line will emerge and will have a slope of +1/2, corresponding to the square root relationship between the noise and signal (Figure 1).
Figure 1 The noise vs. signal plot allows designers to graphically determine four distinct aspects of pixel operations. Source: Etron
With no signal and exposures of zero-length, noise can still be measured in electronic images. While there are a number of contributing components to this noise, it can be collectively called read noise. Contributing to the read noise are 1/F noise and random telegraph signal noise in the source follower amplifiers. Another component is reset noise. Reset noise is the noise associated with the signal node not resetting to the same voltage during each reset operation, as mentioned in part 4 of this article series.
Using correlated double sampling (CDS), reset noise can be effectively removed from an image. CDS uses an amplifier along with sample-and-hold circuits that effectively sample the reset level and then the integrated signal level and differences of one from the other. The resulting signal has the reset noise removed by this method. As shown in part 4, the 3T pixel cannot remove the reset noise at the pixel sensing level. However, the 5T charge-transfer pixel used in rolling shutter mode can remove the reset noise at the pixel sensing level using this differencing combined with sample-and-hold amplifiers.
Dark signal noise
Dark signal is a strong function of temperature, and for a given temperature, it accumulates at a steady rate. For example, for a constant temperature, a doubling of exposure time will result in a doubling of dark signal. For a constant exposure time, approximately every 5-6 °C change makes a 2x factor impact on dark signal.
From a noise perspective, the noise arising from the dark signal has two different components: dark shot noise and dark fixed pattern noise. Like the shot noise associated with light, the dark shot noise is mathematically equal to the square root of the number of thermally-generated electrons within the integration period:
dark shot noise (e-) = SQRT (dark signal(e-))
Dark fixed pattern noise (DFPN) is caused by the non-uniform distribution of the dark leakage current, as shown in part 3 of this article series. Mathematically, DFPN is proportional to exposure time:
DFPN = DSNU * dark signal (e-)
As long as nothing saturates, a doubling of exposure time causes a doubling of the DFPN. For a given exposure time and temperature, this dark fixed pattern is unchanged from frame to frame and can be removed from image frames by “dark subtraction” or “despiking”. An example was shown in the part 3 article.
Dark signal non-uniformity (DSNU) is determined empirically.
Dark shot noise cannot be removed from the image. If practical to cool the sensor, then the dark signal can be made arbitrarily small by cooling. It can add a significant amount of complexity, weight and cost and sharply increase power dissipation, so it’s not practical for many applications.
Fixed pattern noise
If the camera photographs a uniformly illuminated featureless target, then the resulting image should have no discernable features. Any deviation from this ideal case is caused by fixed pattern noise (FPN).
Typically, FPN has two components: optical non-uniformities associated with delivery of focused light to the image sensor with a wide field of view and pixel-to-pixel variation of the photo response of the image sensor. The image sensor manufacturer may specify a pixel level photo response non-uniformity (PRNU) and the optical contributions may be mathematically modeled or empirically determined.
Combined effect of noise components
Mathematically, the combined effect of these uncorrelated noise components is expressed as the square root of the sum of the squares of the individual components.
Total noise = SQRT (system_noise^2 + shot_noise^2 + dark_shot_noise^2 + FPN^2 + DFPN^2)
It’s worth noting that only the system noise is signal level independent. The other terms have either an exposure or time dependency. For instance, shot noise and FPN are both functions of signal charge arising from exposure. Likewise, dark shot noise and DFPN are both functions of dark signal charge, which is dependent on time and temperature.
As a result, it’s possible to plot noise versus signal, as shown in Figure 1, and graphically identify four distinct regimes of operation:
The delineation of each regime is indicated by a change in the slope of the noise curve when plotted using logarithmic axes. The read noise limited regime has a slope of zero. The shot noise limited regime has a slope of +1/2, indicating the square root relationship between the noise and the signal. The fixed-pattern noise limited regime has a slope of +1 and the saturation regime is indicated when the noise rolls off as it begins to saturate the pixels.
From analysis of the same graph, one can graphically determine a number of critical performance parameters such as:
Figure 2 Photon transfer analysis enables graphical measurement of camera gain, photo response non-uniformity, read noise, and saturation level. Source: Etron
This graphical method is called photon transfer analysis and will be discussed in more detail in the next article in this series (Figure 2).
The following actions can be taken to minimize the noise:
Shot noise and read noise are fundamental limits
The only noise components that cannot be removed from an image with non-saturated pixels are the read noise, the image shot noise and the dark shot noise. If it is feasible to cool the sensor, the dark shot noise can be reduced to arbitrarily low levels so as to be a non-factor.
Whether dark subtraction and flat fielding are practical and beneficial depends on the application. For example, a high frame rate video camera may not have much in the way of a dark signal; not much dark signal charge can accumulate in one frame in 1/60 of a second. On the other hand, for a still image of 30 minutes exposure time, a cooled sensor will likely be required.
Fast wide-angle lenses typically introduce significant light intensity variation from center of the field of view to the edges. This variation is fixed from frame to frame as part of a fixed pattern and is proportional to the average intensity of the image. Flat fielding can remove this fixed pattern but may be impractical to apply to a video stream in real-time because the computational bandwidth may exceed the system capabilities in a low-cost consumer product. On the other hand, it may be a small matter to apply to a high-resolution still image.
The sensor’s characteristics and the design of the camera using it will establish the system and read noise characteristics. Contributing factors include sensor design and fabrication technology as well as camera design parameters such as power supply noise and decoupling and PCB signal routing and shielding, particularly the shielding and isolation of digital circuits from the small-signal sensitive analog circuits.
Image sensor’s noise components
The image sensor design and wafer fabrication technology have an enormous impact on the system noise. This system noise can be decomposed into three major components: amplifier noise, reset noise, and column offset noise. Like other uncorrelated noise sources, the combined effect of these sources is again the square root of the sum of the squares:
Sensor system noise = SQRT (reset_noise^2 + column_offset_noise^2 + amplifier_noise^2)
As discussed in part 4 article, the pixel design can affect the reset noise. A charge-transfer pixel can be used in a correlated double sampling scheme to eliminate reset noise present on-chip in the analog processing domain.
Because each column has its own amplifier, the zero-level signal will vary column to column. This column-to-column variation is called column offset noise and often can dominate the sensor’s system noise. Fortunately, it can be removed by subtracting a zero-length exposure from the image.
Image sensor’s fundamental noise floor
The only on-chip noise source that is fundamental and cannot be removed is the source follower amplifier noise. A graph showing the relative magnitudes of these noise sources is shown in Figure 3.
Figure 3 The CMOS offset, reset, and source follower noise are fundamental on-chip noise sources. Source: Etron
In Figure 3, an Iron 55 soft x-ray source has been used to irradiate the sensor. The energy level of the x-ray liberates 1,620 electrons per interacting x-ray. Among other uses, it provides a convenient way to calibrate the digital number (DN) to the electron count; each recorded ‘hit’ is 1,620 electrons. The peaks at 6,480 DN correspond to 1620e- resulting in a calculated camera gain of 0.25 e-/DN.
As Figure 3 reveals, the magnitude of the offset and reset noise versus the “noise floor” represented by the source follower is significant. So, there’s high value in eliminating these noise components if image signal-to-noise ratio (SNR) with low signal intensity is important in your application.
Figure 4 Faint star images obscured by read noise (top) are revealed by combining 64 images (bottom). Source: Etron
An example showing how a faint signal can be “buried” in noise is shown in Figure 4. In this case, by combining 64 images, a factor of 8 reduction of effective read noise is attained by reducing the 7.6e- noise of a single image to 0.97e- in the combined image. More will be explained in future articles about noise calculations and strategies for optimizing signal-to-noise ratio.
This article was originally published on EDN.
Richard Crisp is VP of New Product Development for Etron Technology America.
Other articles in this series: