Subjective Quality Factor

The Subjective Quality Factor (SQF) after EM Grainger and KN Cupery (1972), a psycho-physical factor from the area under the contrast transfer function is obtained. This factor brings the resolution of the eye and thus human visual perception into the contrast transfer function.

General

The SQF was published by EM Grainger and KN Cupery in "Photographic Science and Engineering" in 1972 under the full name “An optical merit function (SQF) which correlates with subjective image judgments”. The SQF was developed as a result of the search for a measurable and easily calculated value that largely corresponds to subjective perception. With the SQF, the subjective image quality, the image impression of people, can be determined with up to 98.8%. This correspondence comes about by comparison with test series of image evaluation by humans.

Background to the SQF

A contrast transfer function describes the transfer, in the broadest sense the image, of an object through an optical medium such as e.g. B. a lens . This function specifies in particular how much contrast is transmitted at a corresponding frequency (black-white transitions). Since the resolution of the human eye is limited by its anatomy , this function must be adapted to this; this is done with the help of the SQF.

application

The SQF can be used as an aid

serve in the design of optical systems.

can be used for a subjective but measurable comparison of different systems.

Description SQF

Illustration of the SQF (according to source: Zeiss)

The SQF refers to the human eye . The resolution of the eye is, however, angle-related, i. H. the resolution becomes smaller with increasing distance. For this reason, the unit line pairs per degree (Lp / deg) is used, which takes into account the viewing distance in relation to the image size. The resolution can be converted into Lp / mm using the angle ratios. The resolution of the eye is 3 Lp / deg to 12 Lp / deg, which describes the spatial frequency. The area under the MTF curve , which corresponds to the SQF, must be as large as possible in this frequency range so that the image appears to be of good quality to the viewer.

The larger the area under the MTF curve, the better the image is perceived. However, the SQF cannot use the image property such as B. the resolution of high or low frequencies can be described. Because the area under two MTF curves can be the same. However, there is a correlation with our subjective perception.

Math background

The SQF results from the area of the MTF curve, the spatial frequencies being plotted logarithmically.
This results in:

Used today:

{\ displaystyle {\ begin {aligned} SQF = K \ int _ {u_ {1}} ^ {u_ {2}} MTF (u) d (\ log (u)) \ end {aligned}}}

${\ displaystyle {\ begin {aligned} K = {\ frac {1} {\ log (4)}} - {\ text {constant for normalization to 1}} \ end {aligned}}}$
${\ displaystyle u_ {1} = 3 \, \ mathrm {Lp / deg}}$
${\ displaystyle u_ {2} = 12 \, \ mathrm {Lp / deg}}$

Original 2-dimensional variant:

{\ displaystyle SQF = K \ int \ limits _ {10} ^ {40} \ int \ limits _ {0} ^ {2 \ pi} OTF (f, \ theta) d (\ log (f)) d (\ theta)}

${\ displaystyle f =}$ Spatial frequency
${\ displaystyle \ theta =}$ azimuthal angles

Measurement option

Test pattern in logarithmic representation for measuring a weighted SQF

The MTF can be determined directly with the SQF weighting using a logarithmically periodic target that is recorded with a camera. A standard MTF evaluation must be carried out from the image recording. The weighted MTF is obtained from this evaluation, so here only the area under the curve has to be determined in order to obtain the SQF.

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Web links

MTF - Modulation transfer Function Explained - Bob Atkins Photography. In: www.bobatkins.com. Retrieved June 23, 2016
Acutance and SQF (Subjective Quality Factor). In: imatest. November 15, 2011. Retrieved June 23, 2016 (American English).
HH Nasse: * How to read MTF curves, part 2. Carl Zeiss, accessed on June 8, 2016 (German).
HH Nasse: How to read MTF curves Part 1 . Carl Zeiss, accessed on June 8, 2016 (German).

Individual evidence

↑ ^a ^b ^c ^d ^e ^f ^g E.M. Grainger, KN Cupery: An optical merit function (SQF) which correlates with subjective image judgments . In: Photographic Science and Engineering . tape 16 , no. 3 , 1972, p. 221-230 .
↑ ^a ^b ^c H.H Nasse: How to read MTF curves, part 2. (PDF) Carl Zeiss, accessed on June 8, 2016 .
↑ Helmut Naumann, Gottfried Schröder, Martin Löffler-Mang: Manual components of optics . Ed .: Helmut Naumann, Gottfried Schröder, Martin Löffler-Mang ,. 7th edition. Hanser, 2014, ISBN 978-3-446-42625-2 , pp. 387 ff .
↑ PGJ Barten: Contrast sensitivity of the human eye and its effects on image quality . Ed .: Knegsel. HV Press, 1999, ISBN 90-90-12613-9 , pp. 156 .

[:0-1] ↑ ^a ^b ^c ^d ^e ^f ^g E.M. Grainger, KN Cupery: An optical merit function (SQF) which correlates with subjective image judgments . In: Photographic Science and Engineering . tape 16 , no. 3 , 1972, p. 221-230 .

[:1-2] H.H Nasse: How to read MTF curves, part 2. (PDF) Carl Zeiss, accessed on June 8, 2016 .

[3] Helmut Naumann, Gottfried Schröder, Martin Löffler-Mang: Manual components of optics . Ed .: Helmut Naumann, Gottfried Schröder, Martin Löffler-Mang ,. 7th edition. Hanser, 2014, ISBN 978-3-446-42625-2 , pp. 387 ff .

[4] PGJ Barten: Contrast sensitivity of the human eye and its effects on image quality . Ed .: Knegsel. HV Press, 1999, ISBN 90-90-12613-9 , pp. 156 .