Photometry and Radiometry

We are the human being living inside the zone of radiation. But all the radiation we can not feel with our eyes. Our eyes can only detect that radiation whose wavelengths are within a range of wavelengths 370 nm to 780 nm. This range is called visible range of wavelength. The radiation within this visible range of wavelength is term as light. Hence, light is an electromagnetic radiation and light has a certain frequency range or wavelength range to be observed by our eyes.

Each radiation has its own energy. Light has the energy to stimulate our eyes. The electromagnetic radiation whose wavelength is more than 780 nm is called infrared radiation that does not stimulate our eyes but stimulates our body as heat. Again the electromagnetic radiation whose wavelength is less than 370 nm is called ultraviolet ray. There are other radiations whose wavelengths are lesser than that of ultraviolet radiation and these radio wave, X-ray, etc. We cannot also observe these radiations as the wavelength of these radiations are less than 370 nm. Within the visible range of radiation, various wavelengths hold the various colors. The range 597 - 577 nm holds yellow which is in the middle of the visible wavelength range.


ColorWavelength RangeFrequency RangePhoton Energy Range
Violet 380–450 nm 668–789 THz 2.75–3.26 eV
Blue 450–495 nm 606–668 THz 2.50–2.75 eV
Green 495–570 nm 526–606 THz 2.17–2.50 eV
Yellow 570–590 nm 508–526 THz 2.10–2.17 eV
Orange 590–620 nm 484–508 THz 2.00–2.10 eV
Red 620–750 nm 400–484 THz 1.65–2.00 eV
The information of the table are collected from wikipedia.org


Photometry

Photometry is a process of measuring light by correlating the visual sensation of a standard human observer. The standard viewer or standard human observer has a visual sensation which is the average of that of hundred numbers of visually fit people.



It is already told that the healthy human eyes are sensitive to the visual range of wavelengths of electromagnetic waves. But it is also true that the human eyes are not equally sensitive to all wavelengths of electromagnetic waves within visual range. For some wavelengths, eyes are more sensitive and for some others, they are less sensitive. Moreover, this sensitivity of eyes for the same wavelength of color can also vary with the intensity of light. That means the visual sensitivity of a color of the particular wavelength may be different in the bright and dim light. Depending on the brightness of the light there are three different types of human vision.

  1. Photopic Vision - while high luminance levels adapt the eyes.
  2. Scotopic Vision - while low luminance levels adapt the eyes.
  3. Mesopic Vision - while intermediate levels of luminance adapt the eyes.
photometry and radiometry

In the photopic vision, the sensitivity of eyes starts increasing from 380 nm and it increases as the wavelength of light increases. At the wavelength of 560 nm, the photopic vision sensitivity reaches its peak and then it starts falling with further increase of wavelength. The wavelength 560 nm corresponds to greenish-yellow color and this is the most eye-catching color in bright light. The photopic vision ends at wavelength 780 nm. The relation between visual sensitivity and wavelength of light is not linear. Hence, the human visual sensitivity to the light can be expressed as a nonlinear function of wavelength V(λ). The function V(λ) is known as relative spectral sensitivity function which is defined as the ratio of the perceived optical stimulus to the incident radiant power as a function of wavelength.



In the scopotic vision (vision in dim light), relation graph between visual sensitivity and wavelength of light is more or less similar to that in photopic vision but the peak of the curve is just shifted to wavelength 507 nm which corresponds to the bluish-green color. That means in the scotopic vision (vision in dim light) the human eyes have the maximum visual sensation to bluish-green color. The relation between visual sensitivity and wavelength in scotopic vision is expressed as another function V’(λ). Hence, above graph shows two functions. V(λ) is for the Photopic vision (vision in bright light) and V’(λ) for Scotopic Vision (vision in dim light). These both functions allow us to derive the photometric quantity. Two graphs have a cross-sectional point at 555 nm. The color corresponding to this wavelength is equally sensitive for Photopic and Scotopic vision.


Radiometry

To relate radiometric quantity to photometric quantity, we have to go for black body radiation. As per practical experiment, the relation between photometric and radiometric has been established. It has been seen that at 2042 K temperature blackbody gives 60 cd/ sq – cm luminance. As the blackbody is a perfect diffuser, it has luminous exitance is 60ᴫ lm/ sq – cm at that temperature. If we plot black body spectral power density (radiometric quantity) we will get a graph for 2042 K radiation. And we multiply the spectral luminous efficacy (V(λ)) with this curve wavelength by wave length for conversion from radiometric to photometric quantity.

The multiplied result gives the new curve of area 0.27598 lumen – Watt/sq – cm. [NB: Radiometric quantity gives W/sq – cm, but when it is multiplied with spectral luminous efficacy then the unit will be lumen – Watt/sq – cm. that is equivalent to luminous exitance in photometry ] So, now equate 60ᴫ lm/ sq – cm to 0.27598 lumen – Watt/sq – cm, we get 60ᴫ/0.27598 = 683 lumen per watt. Thus a constant Km is taken that is equal to 683 lumen per watt in each conversion process. As we calculated

Km in a discrete manner, we can write the conversion equation as,

 

Where, Xv is any quantity in photometry and Xe,λ any quantity in radiometry. In continuous form,

 




This is the process of measuring actual radiation by means of a physical device. Now we can define

the spectral density of a radiometric quantity which has symbol

X as

Where, subscript e for energetic quantity. X can be flux, energy, irradiance or intensity. The photometric quantity corresponding to a radiometric quantity is obtained from

 

This equation is written for the Photopic vision only. But for the Scotopic vision above equation can be written as

 

Km and K'm are proportionality constants. These constants can be defined together with the respective V(λ) functions.
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