Exposure determination for digital recording systems

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Digital recording systems work electronically (ha, ha—of course you know that!) and are therefore fundamentally different from our good old films. Here, exposure determination is all about recording the signal as unaltered as possible, and that means with the highest possible signal-to-noise ratio. The image quality stands and falls with this. Signal means exposure strength (the number of photons), which is read out as electrical voltage and converted into digital data values. Noise is the voltage component generated by the camera electronics that does not originally belong to this signal. The section on the dynamic range of electronic recording systems has shown how to determine both values in practice. The brightness of the tone values now plays only a subordinate role because it can be easily adjusted with the tone value correction or the gradation curves during .raw conversion. The fact that the manufacturers can still stick to the same old exposure metering scheme is only due to one thing: The majority of users create .jpegs in which the tonal values are superimposed with a characteristic curve that closely resembles that of the silver images. However, this incorrect use of digital cameras capable of the .raw format persists.

The light meter is now only an indirect help to us in achieving the goal defined in this way. The tool we stick to is the histogram, which visualizes the relationship between pixel values (signal strength) and digital data values in an actual shooting situation.

A histogram is the graphical representation of the frequency distribution of brightness values.

The histogram shows the statistical brightness distribution of an image in the form of a finely graduated bar chart from black (at the left edge) to white (at the right edge). The horizontal axis plots the brightness, with the height of a bar indicating the number of pixels with each brightness value. The resolution of the horizontal brightness axis normally comprises 256 levels and thus corresponds to an 8-bit image that can store 256 tone values per channel. A solid black image would have only one bar with maximum deflection at the left edge, and a solid white image would have only one maximum bar at the right edge. We don’t encounter anything like that in the wild, however, and that’s why a histogram usually looks like a mountain of tonal values. – Numerous peaks, valleys, and more or less gentle rises show us that certain brightness values occur more frequently in the image than others.

In order to increase the signal-to-noise ratio, we have two adjusting screws: exposure time or aperture, with the extension or enlargement of which we increase the exposure and thus the signal strength (the magnitude on the left side of the signal-to-noise ratio) and the sensitivity setting, with the increase of which we reduce the readout noise (the magnitude on the right side of the signal-to-noise ratio; see section „Determining the dynamic range„). Of course, this raises the question of which end to turn in order to get the best result. The answer is: At both!

To control how far we have to turn, the histogram comes into play. We increase the exposure or sensitivity to such an extent that the tonal value mountain rests far to the right, leaving the highlights barely unclipped. Shots in .jpeg format are not well suited for this enhancement technique known as Expose-To-The-Right (ETTR). They are reduced to 8 bits by the conversion, and the resulting 2⁸=256 brightness levels are usually not enough to catch tonal value breaks (posterization) during the necessary post-treatment.

In the first step, we measure the exposure range of the motif in the classical way, i.e., we determine the exposure values for the darkest and brightest parts of the image that should still show detail and calculate their difference in exposure stops.

The second step should increase the exposure as much as possible because the signal strength has the greatest influence on the signal-to-noise ratio. In order not to cut off the previously determined highlights, it is best to meter them with the spot function. The following limits may be encountered:

• A minimum exposure time that cannot be fallen short of in order not to blur the shot without a tripod (this limit is often quantified with the reciprocal value of the focal length used)
• A maximum exposure time that must be reached in order to sharply freeze a movement
• An aperture setting that is necessary to achieve a certain degree of depth of field

After accounting for all factors, if there’s still a margin on the right side of the histogram, increase the sensitivity in the third step until the highlights stabilize just before the end. Here it pays to know the characteristics of your own camera. Specifically, you should determine whether a) the third-ISO steps have more readout noise than the full ones, leading you to only use the latter, and b) at what sensitivity level the gain drops below one. Increasing beyond this ISO is of little use because you only lose dynamic range without recording a weaker signal. The table in the dynamic range section shows that this value is between ISO 800 and 1600 for the Canon 1D Mark II.

ETTR – Expose To The Right – is recently also known as „HAMSTTR“© – Histogram And Meter Settings To The Right.

Now there are two problems with the histogram. The first issue is that you need a real-time histogram to assess the image before taking it. However, most digital SLR cameras lack this feature due to their design. They use a mirror to redirect the beam path to the viewfinder, revealing the path to the image sensor only at the moment of picture taking. Therefore, their histogram consistently displays the brightness distribution of the previously exposed image, which we can still utilize for image analysis. In this regard, point-and-shoot cameras hold an advantage as their constantly exposed sensor provides real-time information about the brightness pattern. However, even in the DSLR sector, concepts that output a real-time histogram through a technically more complex design are gaining traction. If your own camera model lacks this capability, you will need to achieve the desired outcome using individual images.

The second problem is that the histogram, just like the preview image on the camera display, is calculated from the .jpeg image embedded in the .raw data. So it does not show the distribution of brightness values linearly. And this is not possible at all because the .raw data cannot be used unprocessed and uncorrected, i.e., they are not interpretable. To create the .jpeg preview, the data goes through the following steps: The data undergoes Bayer interpolation (de-mosaiced), projection onto a color space, gamma correction, sharpening, inclusion of a tone curve to enhance contrast, and application of white balance. This raises the highlights to a level we can’t control, and the histogram far too often shows a tonal break where there is none in the RAW data. In many cases, we could easily overexpose by another 1.0-1.5 stops. Because of this, we are unable to accurately determine the extent to which we can increase exposure without risk. Only experience can make up for this to some extent.

To be really safe, we have to get rid of the manufacturer-provided, usually S-shaped, tone curve and gamma correction. Most Nikon and some Canon models accomplish this by presetting a so-called Custom Curve. ToneUp Studio, one of the numerous free RAW converters, offers the possibility of making such a curve available for the camera. To do this, proceed as follows:

• Switch the camera from the usual USB Mass Storage mode to PTP (Picture Transfer Protocol) mode and turn it off
• Connect the camera to the computer via USB cable and turn it on
• Launch ToneUp Studio
• Go to Edit-Preferences and activate the option „Disable Gamma curve when uploading curves“
• Go to File-New Curve. A new window with a linear curve will appear here
• Go to File-Upload Curve
• Turn off the camera and disconnect the USB connection
• Turn on the camera and select Custom Tone Curve in the Optimize Image section

Of course, the images now appear too dark on the camera display, but that doesn’t reflect the final conditions. The .raw converter preview ignores the Custom Curve, presenting a normal gamma-corrected image.

Anyone whose camera cannot handle custom curves can at least come very close to the desired histogram representation by instructing the camera via the various menus to use neutral parameters for the variables contrast, color saturation and sharpness. In addition, you can follow the method suggested by Guillermo Luijk at http://www.guillermoluijk.com/tutorial/uniwb/index_en.htm to also set the in-camera white balance to zero. Running this procedure once per camera takes some time, but it ensures that the histogram aligns with the desired direction of all the setting options.

You often read on the web or in other publications that you should use the exposure setting according to the ETTR method in order to make full use of the available bit range. The idea behind this is that each higher exposure level climbs the next higher bit, and therefore twice as many .raw levels are used to encode the brightness values because they are linear in structure. In a 12-bit file, for example, the highest exposure level has 2,048 RAW levels, the second highest 1,024, the third highest 512, and so on. So it is obvious to assume that the image quality increases with the number of available .raw levels because the transitions between the brightness values become finer.

However, a closer examination of the connection reveals a different reality. Assume, for practical purposes, that the signal strength in the highlights, measured in electrons during one exposure step, is 10,000. The recording noise is then given as √10,000 = 100 electrons. If we assume a gain of 10 – so each higher .raw level counts 10 additional electrons – the recording noise for the assumed signal is 100/10 = 10 .raw levels. Therefore, the linear encoding of the signal in the .raw data largely wastes the .raw steps, as the recording noise is significantly larger than the quantization steps. In this noise, the gained fineness of the transitions is lost. In the shadows, it’s a different story. If we assume a signal strength of 100 electrons for one exposure level there, the recording noise is √100 = 10 electrons. This value translates into a single .raw level at the same gain of 10. So in these low exposure levels, none of the bit levels gained are wasted by quantizing the noise.

The engineers at Nikon have cleverly used this relationship in the structure of their .nef format. They used a lookup table to make the .raw stages less dense in a way that isn’t linear. This table thins out the 4,095 stages of the 12-bit format from bottom to top based on the square-root relationship between noise in the recording and signal strength. Thus, the full number of stages is available in the shadows, while it decreases toward the highlights. Thus, throwing out redundant .raw steps saves digital space without losing visually important information. — Against this background, the expansion to 14-bit A/D converters in the product portfolio seems a bit amusing :-).

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