The dynamic range of electronic image carriers

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We established at the beginning of this section that the dynamic range of an image carrier is the section of the characteristic curve that converts the exposure into sufficiently separated tonal values. The minimum and maximum points limit it. The readout noise on the low exposure side (the point the exposure must exceed in magnitude to leave a trace) and the maximum signal on the high exposure side (the point from which an additional exposure no longer leaves a trace) limit the dynamic range when applied to the characteristic curve of a digital recording system. Both quantities are determined in electrons. The technical dynamic range is defined as such, and its significance lies in the fact that a camera’s capabilities in this area are frequently subject to various constraints.

The lower limit of the dynamic range – Noise

Due to thermal effects, every sensor produces an unwanted excitation of the electrons, the so-called noise. This typically refers to the unwanted portion of an acoustic or electromagnetic signal that does not originate from the source. Isolating this part and making it audible through a loudspeaker strongly suggests naming the phenomenon „noise“. After Walter Schotty first described noise in 1918 as a measurable fluctuation in electricity, the sciences succeeded in discovering numerous physical types of noise. Today, researchers continue to intensively study many of these types of noise. We quantify noise by measuring its component in the useful signal and expressing it as the signal-to-noise ratio, also referred to as SNR, S/N, or simply signal strength/noise. Given the diverse components of electronic recording technology, it’s unsurprising that electrical noise also plagues digital photography. For the analysis of an electronic recording system, the noise types readout noise, recording noise and fixed pattern noise play the most important role. They are distributed over the characteristics of the system, as shown in figure 37.

Unwanted electrical activity creates noise, which is an inevitable component of all electronic data processing, including digital photography.

Readout noise

Readout noise usually includes the noise of the readout unit of the pixels, the noise of the downstream voltage amplifier and the noise of the A/D converter. Similar to the flat area in the photon transfer curve, readout noise essentially represents the lower limit of the usable area on the characteristic curve, which must first be overcome by a sufficiently strong exposure. Therefore, it can also be thought of as a noise carpet. In terms of silver film, this would be the base density.

The following components play a role. First, there is the fact that the pixels are not all read out at the same time. The ones at the bottom get their turn slightly later than the ones at the top and for this reason have a slightly higher pixel value. Then there is a variation or „uncertainty“ in the conversion of the (analog) voltage value of the pixels to the (digital) binary value. This is because converting the same voltage value will not always yield the same binary value. Last, the sensor and the A/D converter introduce additional random signals that are quantized along with the voltage value. For these reasons, the readout noise is highly camera-dependent.

Shot noise

Shot noise (also called photon noise) is a type of noise generated by the image signal itself because most light sources emit photons in a random distribution. For this reason, it cannot be avoided or removed and sets the absolute limit of what can be achieved in terms of noise-free performance. Related statistics say that the uncertainty in the number of photons in a sample (the noise) is equal to the square root of its total number. In figure 38 we see this relationship for a sensor with 4 µm x 4 µm pixels and one with 8 µm x 8 µm pixels. The first receives 4 x4 = 16 photons with a noise component of √16 = 4 photons. Consequently, its SNR is 16/4 = 4. The second sensor receives 16 x16 = 64 photons with a noise component of √64 = 8 photons. Here, the signal-to-noise ratio is 64/8 = 8. Therefore, when the pixel size doubles, the signal-to-noise ratio also doubles.

Fixed pattern noise

Fixed pattern noise is caused by sensitivity variations between individual pixels. Usually known as Photo Response Non-Uniformity (PRNU), it directly correlates with the strength of the input signal. For this reason, the photon transfer curve in this area has a slope of 1. This type of noise can be largely eliminated with the aid of a reference image (flat field image), which is obtained by taking the difference between two or more exposures at the same exposure time and ISO setting.

Random pattern noise

Random pattern noise is characterized by fluctuations in brightness and chrominance above and below the actual intensity. Therefore, we divide it into luminance noise, also known as brightness noise, and chrominance noise, also known as color noise. Luminance noise is visible as a speckle pattern of lighter and darker areas and therefore strongly resembles the graininess known from silver film. Chrominance noise appears as colored blobs (often magenta or green) that cover the image like small ink blots. People fondly refer to it as „the typical digital noise.“ Despite the high sensitivity of our visual system to variations in brightness, color noise appears to most viewers as much more distracting. Fortunately, digital SLR cameras today suffer more from luminance noise than chrominance noise, and if their images do show the more noticeable color noise, it is far less pronounced than in consumer point-and-shoot cameras.

Dark noise

Dark noise, also known as fixed pattern noise or dark current, arises from the pixels of the image sensor reacting not only to incident light but also to thermal influences. These influences include the ambient temperature and the heat the camera generates during operation. The individual pixels respond differently to these temperature influences. Dark noise is particularly unpleasant in images with low contrast and long exposure times because it increases in proportion to the exposure time. The camera electronics can almost completely eliminate it by automatically subtracting a dark image with the exact noise pattern from the original image. Pellet elements actively cool extremely high-quality imaging sensors in the field of astrophotography. Cooling by 7° C halves the dark noise.

The upper limit of the dynamic range – Maximum signal

The signal strength is directly dependent on the strength of the exposure, because the more photons that act on the sensor, the more electrons it releases. The exposure strength in turn depends on the set sensitivity (ISO value), because with each doubling of the sensitivity we have to halve the exposure to get a correctly exposed image. Indirectly, another factor also plays a role, namely the number of electrons that a pixel can store, its so-called full well capacity.

Sensitivity adjustment

A CCD or CMOS chip actually has only one fixed sensitivity. When we alter the ISO value, the electronics perform two functions: first, it modifies the voltage amplified by the readout amplifier between the chip and the A/D converter, which is not of interest to us, and second, it modifies the process by which the A/D converter transforms electrons into data values, which is of great interest to us. Both values are called „gain“ and to distinguish the second from the first, we think of it better as a conversion factor. Nevertheless, when you read about „gain“ on the web or elsewhere, it usually refers to this concept. If we double the sensitivity, the conversion factor is halved, and vice versa. This adjustment is the crucial point. If we briefly consider the relationship between exposure and sensitivity, we can understand it.

The shift in sensitivity essentially indicates that either a more intense exposure is required or a slightly reduced exposure is adequate to achieve a specific tonal value. Thus, at ISO 200, the image carrier must be exposed only half as much as at ISO 100 in order to exhibit the same blackening (if we think of this in analog terms in this digital section). Conversely, twice the exposure is necessary. The following expression mathematically reveals this reciprocal relationship between exposure and sensitivity, where H represents the exposure in lux-seconds needed to achieve the specified tone value:

Formula 14

Higher ISO values therefore do not make the sensor more sensitive but lead to ever lower signal strength due to the reciprocal relationship between sensitivity and exposure strength. To maintain the same data value or tone value after quantization, halving the conversion factor is necessary. In other words, the increase in sensitivity is realized by requiring fewer electrons to fill a data value: At ISO 100, data value 1000 consists of 13,020 electrons (1,000*13.02 = 13 020); at ISO 200, the same data value consists of 6,510 electrons (1,000*6.51 = 6510).

Full Well Capacity

At the upper end of the dynamic range, we are dealing with a strong exposure and a lot of light. However, a lot of light causes the semiconductor to release a large number of electrons, which the downstream computing units must temporarily store before digitising the information. The capacitors directly coupled to the pixels accomplish this. Their capacity determines the maximum light intensity that the technology can integrate in one exposure, and it is referred to as full well capacity. Problem recognized, problem solved! – So if we want to extend the dynamic range upward, we only need to increase the capacitor accordingly! To paraphrase Radio Yerevan, „the answer is yes in principle, but there is a catch“. Unfortunately, this simple equation only works up to a certain size because, due to technical limitations of the number of layers in the production of integrated circuits, the size of the capacitor is directly proportional to the area of the pixel. Now you might object that the pixel area describes the size of the capacitor only in two dimensions (length x width), and therefore one could simply fabricate it deeper. Unfortunately, there are two reasons to oppose this approach. First, the risk of short circuits between neighboring pixels would increase. On the other hand, vertically larger (deeper) capacitors would block the incident light.

The full well capacity is basically a function of the pixel area and is between 800 and 1600 electrons per µm².

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