Doug Kerr
Well-known member
An important property of a photographic image presented for viewing is what we commonly speak of as "sharpness". Bu if we are to go beyond "I can tell sharp when I see it", we need to consider what does that mean? What is "sharpness" a measure of? What unit is it quantified in? If we wanted to determine in a laboratory what "sharpness" would a certain imaging chain (camera, postprocessing, rendering on-screen or in a print) be expected to give, what principle of measurement and analysis would we use?
We often think that sharpness is perhaps another term for resolution, but we have the very same problems with that term.
It is generally considered that whatever property "sharpness" is, it is determined by the modulation transfer function (MTF) of the imaging system. The MTF, in graphic form (in the form of interest here) is a plot of what would be called in electrical engineering the "transmission" through the system of detail (conveyed by variation in luminance) as a function of the spatial frequency of the variation of luminance. In fact the quantity of interest is the ratio of:
• The ratio of the maximum luminance (or illuminance) of the image of a test pattern to its minimum luminance (or illuminance) (said to be the the modulation depth) at the output of the system (for example, on the sensor of a camera, or on the delivered print).
to
• The ratio of the maximum luminance (or illuminance) of the test pattern to the minimum luminance (or illuminance) (the modulation depth), which is of course at the input to the system.
This way this ratio varies with spatial frequency is called the modulation transfer function (MTF). The ratio itself at any given spatial frequency is said to be the value of the MTF at that frequency, or just the MTF at that frequency. Thus, the MTF is the plot of how the MTF varies with spatial frequency. Wonderful!
This visual impression of "sharpness" is conceptually affected by the shape of this entire curve. But we are anxious to have a single metric, a "figure of merit", for sharpness.
Sometimes we use the spatial frequency at which the MTF drops to 50% of its value at low spatial frequencies. Sometimes we use the spatial frequency at which the MTF drops to 50% of its maximum value over all spatial frequencies. Sometimes we use the spatial frequency at which the MTF drops to 20% of its value at low spatial frequencies.
In 1972, Granger and Cupery proposed a "merit function", a single value, objectively determinable, that seemed to correlate well with subjective assessments of "sharpness" by human viewers. They called it the Subjective Quality Factor (SQF), notwithstanding the fact that it is:
• An objective, not subjective, metric, and
• It only assesses one aspect of the broader matter of the overall "quality" of an image ("sharpness").
Here, I will describe the concept behind this metric.
The spatial frequency response of the human eye
We are familiar with the fact that the response of the human eye to light varies with the wavelength (and thus frequency) of the light.
Less well known is that the "sensitivity" of the eye to detail (that is, to variations in luminance) also varies with the spatial frequency of the detail. It is at a maximum at about 6 cycles per degree, and is in fact rather low below 3 cy/deg and above 12 cy/deg. This variation is known as the Contrast Sensitivity Function (CSF) of the eye.
The findings of Granger and Cupery
A simplified form of what Granger and Cupery determined is that the human assessment of the sharpness of an image (as a single-number "score") is very nearly proportional to the area under the MTF curve (when we use a logarithmic scale for spatial frequency) over the range of spatial frequencies from 3 cy/deg through 12 cy/deg.
More precisely, the human assessment of the sharpness of an image (as a single-number "score") is very nearly proportional to the integral (over the entire range of spatial frequencies of any interest) of the product (at each spatial frequency) of the CSF of the eye and the MTF of the system of interest.
And today, when the SQF of an imaging system is determined by laboratory testing, the analysis of the results follows the "very simple" model, the "precise" model, or something in between.
The role of the print size and viewing distance
We might think that it would be nice to determine the SQF of the camera (to the digital output), and then we could somehow transform that to the context of a print at a certain size viewed from a certain distance.
But the definition is based on visual perception, which works in angular terms, and thus we cannot determine the SQF of a camera (let's say just up to the digital image, not consideration the effect of the display or the printer) without presuming some viewing situation.
How that is done is rather curious, and I will cover it in part 2 of this article.
[to be continued]
Doug
We often think that sharpness is perhaps another term for resolution, but we have the very same problems with that term.
It is generally considered that whatever property "sharpness" is, it is determined by the modulation transfer function (MTF) of the imaging system. The MTF, in graphic form (in the form of interest here) is a plot of what would be called in electrical engineering the "transmission" through the system of detail (conveyed by variation in luminance) as a function of the spatial frequency of the variation of luminance. In fact the quantity of interest is the ratio of:
• The ratio of the maximum luminance (or illuminance) of the image of a test pattern to its minimum luminance (or illuminance) (said to be the the modulation depth) at the output of the system (for example, on the sensor of a camera, or on the delivered print).
to
• The ratio of the maximum luminance (or illuminance) of the test pattern to the minimum luminance (or illuminance) (the modulation depth), which is of course at the input to the system.
This way this ratio varies with spatial frequency is called the modulation transfer function (MTF). The ratio itself at any given spatial frequency is said to be the value of the MTF at that frequency, or just the MTF at that frequency. Thus, the MTF is the plot of how the MTF varies with spatial frequency. Wonderful!
This visual impression of "sharpness" is conceptually affected by the shape of this entire curve. But we are anxious to have a single metric, a "figure of merit", for sharpness.
Sometimes we use the spatial frequency at which the MTF drops to 50% of its value at low spatial frequencies. Sometimes we use the spatial frequency at which the MTF drops to 50% of its maximum value over all spatial frequencies. Sometimes we use the spatial frequency at which the MTF drops to 20% of its value at low spatial frequencies.
In 1972, Granger and Cupery proposed a "merit function", a single value, objectively determinable, that seemed to correlate well with subjective assessments of "sharpness" by human viewers. They called it the Subjective Quality Factor (SQF), notwithstanding the fact that it is:
• An objective, not subjective, metric, and
• It only assesses one aspect of the broader matter of the overall "quality" of an image ("sharpness").
Here, I will describe the concept behind this metric.
The spatial frequency response of the human eye
We are familiar with the fact that the response of the human eye to light varies with the wavelength (and thus frequency) of the light.
Less well known is that the "sensitivity" of the eye to detail (that is, to variations in luminance) also varies with the spatial frequency of the detail. It is at a maximum at about 6 cycles per degree, and is in fact rather low below 3 cy/deg and above 12 cy/deg. This variation is known as the Contrast Sensitivity Function (CSF) of the eye.
The findings of Granger and Cupery
A simplified form of what Granger and Cupery determined is that the human assessment of the sharpness of an image (as a single-number "score") is very nearly proportional to the area under the MTF curve (when we use a logarithmic scale for spatial frequency) over the range of spatial frequencies from 3 cy/deg through 12 cy/deg.
More precisely, the human assessment of the sharpness of an image (as a single-number "score") is very nearly proportional to the integral (over the entire range of spatial frequencies of any interest) of the product (at each spatial frequency) of the CSF of the eye and the MTF of the system of interest.
And today, when the SQF of an imaging system is determined by laboratory testing, the analysis of the results follows the "very simple" model, the "precise" model, or something in between.
The role of the print size and viewing distance
We might think that it would be nice to determine the SQF of the camera (to the digital output), and then we could somehow transform that to the context of a print at a certain size viewed from a certain distance.
But the definition is based on visual perception, which works in angular terms, and thus we cannot determine the SQF of a camera (let's say just up to the digital image, not consideration the effect of the display or the printer) without presuming some viewing situation.
How that is done is rather curious, and I will cover it in part 2 of this article.
[to be continued]
Doug