Persons who want to understand when their eyes may be misleading them.
A readable, yet rigorous discussion of the relationship between signal, contrast, and noise.
Learn more about noise and CMOS technology, read Changing the Game.
For quantifying the ability of a camera to detect a signal (i.e., “Can I see my signal?”) and for defining the precision of the measurements made with a detector, the signal-to-noise ratio (SNR) of a camera is an extremely powerful tool. Yet there are cases when SNR cannot provide the most meaningful data.
Imagine a photograph of a cityscape on a foggy day. The image is bright and would likely have a high SNR, but our ability to “see” the skyline is impaired because of the lack of contrast. Contrast is a general term that gets to concept of “visibility”: Can I distinguish the signal of interest from the background signal? When we have an abundance of photons, i.e. in the shot noise regime, sensitivity becomes the ability to discriminate between two different, distinct levels of signal and in many cases the most important two levels are signal and background.
More than any other noise factor, background in the sample has been overlooked as a relevant term in considering sensitivity. This consideration is especially relevant for biological samples.1 We know that background affects SNR, but it also affects contrast.
Fundamentally, because of photon shot noise, wherever there is background signal there is also background noise, yet this also has a camera component. Similar to SNR equations, it’s possible to have contrast-to-noise (CNR) equations: CNR = QE * S / [Nb + Ns] where Nb is noise of the background and Ns is noise of the signal.
An easy way to visualize the difficulty that background and background noise poses in imaging is depicted in Figure 1. This figure shows that CNR is especially relevant when considering background in the context of choosing between an EM-CCD and the ORCA-Flash4.0 (older model of the ORCA-Flash 4.0 V3). We know that the cross-over intensity into the shot noise regime is a function of the read noise (Nr) of camera. Due to the great reduction in Nr with Gen II sCMOS cameras, in most fluorescence microscopy, both the signal and the background now reside in the shot noise (or eQE) domain. In this regime, because of EM gain noise (Fn), the noise of the signal and background detected with an EM-CCD will be higher than with the ORCA-Flash4.0 resulting in reduced CNRs.
Contrast and noise. (A) The graph depict the signal intensity and noise of the line through the inset grey squares and demonstrates the problem with background in the context of contrast. Contrast in an image is the perceived ability to distinguish between the background and the signal of interest. If both were noiseless, this would not be too difficult even if the signal was nearly identical to the background. However, camera noise and photon shot noise create an overlap in the signal and background regions with similar intensity, making it difficult to separate signal from background.
(B) Because of Fn the noise in imagestaken with an EM-CCD is greater than those from an ORCA-Flash4.0. Thus, when background is high, separation of signal from background in an EM-CCD image will be more difficult.
CNR also describes how we perceive the quality of the image. A good rule of thumb is that a pixel with a CNR of 2 can be detected by eye. On the low side, a pixel with a CNR of 1 can be just barely detected. However, this is a CNR for a single pixel of signal relative to background. Images with a CNR < 1 can show structures at reduced spatial or temporal resolution. When pixels of much lower CNR are grouped together, there is an effect called spatial pixel averaging.
When we look at images our brain performs complex functions including integrating large areas of similar signal, looking for patterns, symmetries and edges. For this reason, if we have a collection of adjacent pixels even with a very poor CNR (< 1), we may still be able to detect them visually.
Mathematically, visibility is improved by the square root of the number of pixels averaged.2 In a quantitative imaging experiment, measurements are made by well-defined algorithms, not by eye. But we can only view images in any publication or presentation with our eyes and therefore we must be aware of the spatial averaging or integration that is happening automatically in our brain.
Along with this automatic visual processing, images that are displayed are subject to many variables intrinsic to the display format (e.g., quality of the monitor, intensity scaling of the image data, printing technique, etc.) that can affect the perceived contrast. For these reasons, determinations of the quality of an image from a given camera should never be assessed exclusively by eye or on image files that have been subject to lossy compression, such as jpeg.
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