# Photometric Calibration

## Background

Digital cameras of today have CMOS based sensors to convert the light incident (irradiance) on them into digital values. These sensors have a characteristic Inverse Camera Response Function (ICRF) which maps the irradiance to the pixel value generated (typically between 0-255). In the cameras we use, the ICRF curve is adjusted so that the color reproduced in the digital pixels resemble what our human eye can see. This is particularly useful for consumer products but when one is using cameras for scientific applications ranging from vision systems in autonomous cars to 3D reconstruction, it is imperative to have the true pixel value to be calibrated to the true irradiance values on the CMOS sensor.

## Problem

The goal is to obtain the absolute value of light intensity and calibrate the CMOS sensor output of the camera to match the said absolute value of light intensity. Highest accuracy and precision are desired.

There are two ways of approaching this problem:

1. Method I: Get the value of the intensity of light of the surface using Photometers/Lux meters/Radiometers.
2. Method II: Use a standardized light source with controllable wavelength and intensity.

A comparative overview of the two stated methods has been given below in Table 1, each advantage is given an unweighted score of 1: Table 1

Method I Method II
Principle of Operation Uses a transducer to convert light intensity to a digital signal. Uses a transducer to convert digital signals into light waves.
Sensor/Transducer Silicon(doped) Photodiode Silicon(doped) LED / Tungsten Filament
Cost $- Cheap$ - Expensive
Luminous efficiency error 9% - High 0.001% - Low
Dependence on ambient light In-effective/false positives under fluorescent lighting Independent of ambient lighting
Response time 5 s 0.500 s
Characteristics of oblique incidence/ Luminance Spatial uniformity Incidence: 10° ±1.5% / 30° ±3% / 60° ±10% /80° ±30% Spatial Uniformity: >94% over 360° x 200° field of view
Spectral range Lux meter: 1; Photometer: 850 nm to 940 nm Visible, 850 nm to 940 nm
Spectral mismatch 1% >0.00001%
Luminescence range 0.0 to 999 cd/m2 0 to 700 cd/m2
Typical application Lux meter: Ambient light; Photometer/Radiometer: Color of surfaces. Calibration of Lux meters, Photometers, Radiometers, Cameras & other optical equipment.
Operational features Comparatively less stable output; Needs regular calibration; Integration with desktop on select models. Precise control. Easy integration with desktop. Long life. Stable output
Total score 2/10 7/10

## Result

Method II is the most desirable way to go about solving the problem at hand.

## References

Use these for choosing the type of validation of photometric calibration:

1. https://www.labsphere.com/site/assets/files/2928/pb-13089-000_rev_00_waf.pdf
• http://ericfossum.com/Publications/Papers/1999%20Program%20Test%20Methodologies%20for%20Digital%20Camera%20on%20a%20Chip%20Image%20Sensors.pdf
• http://sensing.konicaminolta.us/2013/10/measuring-light-intensity-using-a-lux-meter/
• http://tmi.yokogawa.com/products/portable-and-bench-instruments/luxmeters/digital-lux-meters/
• http://ens.ewi.tudelft.nl/Education/courses/et4248/Papers/Niclass12.pdf
• http://photo.net/learn/dark_noise/
• http://ro.ecu.edu.au/cgi/viewcontent.cgi?article=2497&context=ecuworks
• http://personal.ph.surrey.ac.uk/~phs1pr/mphys-dissertations/2007/Wallis.pdf

## Foot Notes

LED light source is preferred over tungsten filament based source as it has the below-stated superiority:

1. Life
2. Heat/IR – minimum
3. Multitude of Wavelengths generated
4. Precise selection of Wavelength & Intensity