Contrast Sensitivity
Build a contrast-sensitivity function and trapezoidal area in log10 frequency/log10 sensitivity space from measured Michelson thresholds.
Description
Contrast sensitivity is the reciprocal of a threshold contrast.
Contrast sensitivity is the reciprocal of a threshold contrast. An area in log-frequency versus log-sensitivity space summarizes the supplied curve on logarithmic scales.
The tool returns sensitivities (sensitivities); logFrequencyLogSensitivityArea (log frequency log sensitivity area). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Contrast Sensitivity
Use Contrast Sensitivity when you already have spatialFrequenciesCyclesPerDegree, michelsonThresholds and want sensitivities, logFrequencyLogSensitivityArea. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Contrast Sensitivity and understand its results
- Enter spatialFrequenciesCyclesPerDegree, michelsonThresholds using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read sensitivities, logFrequencyLogSensitivityArea. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| spatialFrequenciesCyclesPerDegree | Spatial frequencies cycles per degree | list of number | Required |
| michelsonThresholds | Michelson thresholds | list of number | Required |
Use increasing positive cycles-per-degree frequencies and thresholds in (0,1]. Trapezoidally integrate the logarithmic coordinates.
sensitivity = 1/MichelsonThreshold; area = ∫log10(sensitivity) dlog10(frequency) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"spatialFrequenciesCyclesPerDegree": [
1,
2,
4
],
"michelsonThresholds": [
0.1,
0.05,
0.1
]
},
"output": {
"sensitivities": [
10,
20,
10
],
"logFrequencyLogSensitivityArea": 0.692679049617419
}
}Limitations and assumptions
The curve is supplied rather than estimated from trials. The area depends on the measured frequency range and is not a linear-scale area.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Visual Acuity logMAR: Score acuity using a caller-specified starting score and per-letter increment, then convert to decimal acuity; the chart scoring convention must be supplied. Spectral Edge Frequency: Locate a requested integrated PSD fraction by trapezoidal integration and within-bin linear-density inversion; not a percentile of frequency samples.
Methodological background: Digital Library of Mathematical Functions: Quadrature.1
References
-
Digital Library of Mathematical Functions: Quadrature — National Institute of Standards and Technology
Similar or alternative tools
- Visual Acuity logMAR
Score acuity using a caller-specified starting score and per-letter increment, then convert to decimal acuity; the chart scoring convention must be supplied.
- Spectral Edge Frequency
Locate a requested integrated PSD fraction by trapezoidal integration and within-bin linear-density inversion; not a percentile of frequency samples.