# Sharpness: What is it and How it is Measured

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## Measuring Sharpness

Figure 1. Bar pattern: Original (upper half of figure) with lens degradation (lower half of figure)

Sharpness determines the amount of detail an imaging system can reproduce. It is defined by the boundaries between zones of different tones or colors.

Figure 2. Sharpness example on image edges

In Figure 1, sharpness is illustrated as a bar pattern of increasing spatial frequency. The top portion of the figure is sharp and its boundaries are crisp; the lower portion is blurred and illustrates how the bar pattern is degraded after passing through a lens.

Note: All lenses blur images to some degree.

Sharpness is most visible on features like image edges (Figure 2) and it can be measured by the edge (step) response.

Several methods are used for measuring sharpness that include the 10-90% rise distance technique, modulation transfer function (MTF), special and frequency domains, and slanted-edge algorithm.

### Rise Distance and Frequency Domain

A successful technique for measuring image sharpness is to use the “rise distance” of a tone or color edge.

Figure 3. Illustration of the 10-90% rise distance on blurry and sharp edges

With this technique, sharpness can be determined by the distance of a pixel level between 10% to 90% of its final value (also called 10-90% rise distance; see Figure 3).

Although rise distance is a good indicator of image sharpness, it also contains a strong limitation in that there is no easy method to calculate the rise distance of a complete imaging system from the rise distance of its components (i.e., lens, digital sensor, and software sharpening).

To sidestep this issue, measurements can be made in the frequency domain where frequency is measured in cycles or line pairs per distance (millimeters, inches, pixels, image height, and sometimes angle [degrees or milliradians]).

Figure 4. Measuring sharpness in the frequency domain

When measuring sharpness in the frequency domain, a complex signal (audio or image) can be created by combining signals consisting of pure tones (sine waves), which are characterized by a period or frequency (Figure 4). Furthermore, frequency and spatial domains are related by the Fourier transform:

$$F(x)=\int_{-\infty}^{\infty}f(t)e^{-i\omega t}dt$$$$f(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}F(\omega)e^{i \omega t}d\omega$$

Where

Frequency = f = 1/Period (shorter period = higher frequency)t = timeω = 2πf

Figure 5. High frequencies correspond to fine in the spatial and frequency domain

The better the system response at high frequencies (short periods), the more detail the system can convey (Figure 5). System response can be characterized by a frequency response curve, F(f).

Note: High frequencies correspond to fine detail.