Tonal Range

Vincent Bockaert, 123di.com

The tonal range of a digital image is the number of tones it has to describe the dynamic range. These conceptual examples show that an image with a large dynamic range can have a narrow tonal range and an image with a low dynamic image can have a wide tonal range.

Wide Tonal Range
Narrow Tonal Range
High Dynamic Range
Low Dynamic Range

Dynamic Range and Tonal Range of the Sensor

The dynamic range and tonal range of a sensor are related. If a sensor has a dynamic range of say 1000:1 AND it has an ADC of at least 10 bit, it automatically has a wide tonal range. If a sensor with a 10 bit ADC is able to output about 1,000 different tones, the sensor must have a dynamic range of at least 1000:1. This is because the sensor is linear and an ADC samples in equal steps.

Dynamic Range and Tonal Range of the Image

Once you apply a tonal curve to the linear sensor data, the dynamic range and tonal range of the image can vary independently, depending on what tonal curve you apply. The tonal curve can compress the dynamic range, the tonal range, or both[1].

When shooting in JPEG, the rather contrasty tonal curves applied by the camera may clip shadow and highlight detail which was present in the RAW data. RAW images preserve the dynamic range captured by the sensor and allow you to compress the dynamic range and tonal range by applying a proper tonal curve so that the whole dynamic range is represented on a monitor or print in a way that is pleasing to the eye. This is similar to the more extreme example below which shows how the larger dynamic range and tonal range of a 32 bit floating point HDR image were compressed.

Dynamic Range and Tonal Range of a Monitor or Printer - Compression

Monitors and printers have a limited dynamic range. Therefore a tonal curve is applied to the linear raw data to compress the dynamic range so that it fits in the dynamic range of the monitor or printer. The tonal curve is chosen so that detail is preserved where it is most noticeable. As a result, the image looks pleasing to the human eye and the perceived dynamic range is higher, even on a limited dynamic range print.

A. Shadow detail captured
B. Highlight detail captured
C. Shadow and highlight detail combined; but h:s is reduced

In this scene, the shadows were about 2,000 times darker than the highlights (11 stops). As explained in the dynamic range topic, a digital camera could capture either image A or image B. In image A, the highlights are clipped because the long exposure needed for the shadow detail to be captured, caused the highlight pixels to overflow. In image B, to prevent the highlights from being clipped, exposure had to be so short that the sensor did not receive enough photons to capture shadow detail, resulting in clipped shadows.

In Adobe Photoshop CS2 you can combine several exposure bracked images into a high dynamic range image. How do we represent such a high dynamic range on a limited dynamic range monitor or printer? The answer is "compression".

In the histogram of images A and B, the red and blue areas show the unclipped shadow and highlight detail respectively. Compressing both areas by describing them with fewer tones allows both areas to be combined into a single image that looks pleasing on a monitor or print. The catch is that in the actual scene the values of the highlights were about 2000 times stronger than the shadows, while on the monitor, and especially on the print, h:s will be much lower. When viewing Image C on a monitor, it has a high perceived dynamic range because it looks as if the whole dynamic range of the scene was captured in single exposure by a camera with a very high dynamic range. Tonal compression is better done in high bit environments as it avoids posterization.

Technical Footnotes

  1. (1) Here the analogy with film applies. For instance, positive (slide) film has a wider density range but less exposure latitude, while negative film, has a narrow density range, but more exposure latitude.
This article is written by Vincent Bockaert,
author of The 123 of digital imaging Interactive Learning Suite
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