Spatial Frequency

When a person looks at two lights shining at a distance, he can distinguish between them because the light from each source travels through the eye and hits a different set of light-sensitive cells (photoreceptors). Once the light moves closer to each other, they hit the photoreceptors in proximity (see image), and beyond a certain distance, the brain is unable to distinguish between them and starts to interpret them as one light source. The angle between those two rays of light at which a person loses the ability to distinguish between the two lights is 1/60th of a degree, also known as one arc minute; it plays a major role in understanding spatial frequency.

The diagram shows the difference in image formation on the photoreceptors (in fovea) when the lights are at varying distances from each other. Once the lights get too close the brain starts to interpret the images as one because it falls on the single photoreceptor and the brain is unable to distinguish between them.

Spatial frequency refers to the level of details present in an image (stimulus) per degree of visual angle. A letter with small details and sharp edges contains higher spatial frequency as compared to a simplified letter with round edges. It is expressed in the number of cycles of alternating dark and light bars (the black and white parts of the letter in case of type) per degree of visual angle also known as “cpd”. Humans can perceive a maximum of 60 cycles per degree(cpd) and information beyond that limit is filtered out.

Spatial frequency is determined by the number of cycles of alternating dark and light bars per degree of visual angle. Figure (a) has more alternative light-dark bars per degree of the visual angle. Hence it is of higher spatial frequency than (b). Source: https://www.ucalgary.ca/pip369/ mod4/spatial/frequency1

The visual angle becomes smaller with the increase in the distance, moving away from a particular image increases the high spatial frequency content. It has a direct impact on text viewed at a distance, once the distance increases the spatial frequency of the text increases with it and once it reaches above 60 cpd, the brain starts to filter out the high-frequency elements like serifs, sharp edges and corners.

Samples of the filtered letters. The spatial frequency is given underneath each letter. The frequency increases with the increase in the number of details seen by the human eye. The contour/outlines have the highest frequency which facilitates the viewing of the correct shape of the letter. Source: Chung, S.T., Legge, G.E., & Tjan, B.S. (2002). Spatial-frequency characteristics of letter identification in central and peripheral vision. Vision Research, 42