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Chapter: 2 General physics
    Section: 2.5 Radiation and optics
        SubSection: 2.5.3 Photometry

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2.5.3 Photometry

The results of photometric matching experiments show that radiation may be evaluated in terms of visual effect by means of a quantity known as luminous flux, γ, which is related to e, λ(λ), the spectral power distribution of the radiation, by an equation of the form


   

 

v = Km

eλV(λ)dλ    ...(1)

 

0


where Km is a constant, and V(λ) a function representing the wavelength-dependent sensitivity of the eye. The exact shape of V(λ) depends on the observer, but in order to provide a precise quantitative basis for photometry, an agreed set of values was recommended for adoption by the Commission International de lÉclairage (CIE) in 1924, and accepted by the Comité International des Poids et Mesures (CIPM) in 1970 (see section 1.1.2).

The following table gives the values of this function at 10 nm intervals. For the complete tabulation at 1 nm interval refer to ISO/CIE 10527 (1991).



Photopic spectral luminous efficiency function V(λ)

λ/nm

V(λ)

λ/nm

V(λ)

λ/nm

V(λ)

λ/nm

V(λ)

λ/nm

V(λ)

360

0.000 004

460

0.060 000

555

1.000 000

650

0.107 000

750

0.000 120 

370

0.000 012

470

0.090 980

560

0.995 000

660

0.061 000

760

0.000 060 

380

0.000 039

480

0.139 020

570

0.952 000

670

0.032 000

770

0.000 030 

390

0.000 120

490

0.208 020

580

0.870 000

680

0.017 000

780

0.000 015 

400

0.000 396

500

0.323 000

590

0.757 000

690

0.008 210

790

0.000 007 

410

0.001 210

510

0.503 000

600

0.631 000

700

0.004 102

800

0.000 004 

420

0.004 000

520

0.710 000

610

0.503 000

710

0.002 091

810

0.000 002 

430

0.011 600

530

0.862 000

620

0.381 000

720

0.001 047

820

0.000 001 

440

0.023 000

540

0.954 000

630

0.265 000

730

0.000 520

830

0.000 000 

450

0.038 000

550

0.994 950

640

0.175 000

740

0.000 249

 

 

The magnitude of the unit of luminous flux, the lumen, is determined by assigning a value to Km of equation (1). However, for historical reasons the SI base unit for photometry is the unit of luminous intensity, the candela or lumen per steradian; the formal definition (16th CGPM, 1979) appears in section 1.1.1. The rounded frequency 540 × 1012 Hz corresponds to a wavelength of 555.016 nm in standard air, whereas Km occurs at 555 nm exactly. Thus Km is precisely 683.002 lmW−1, although the value 683 lm W−1 is sufficient for all practical purposes.

The spatial properties of light are described in photometry by quantities analogous to those used in radiometry (see section 2.5.2), with luminous flux replacing radiant power. The same symbols are used for corresponding quantities, distinguished where necessary by the suffixes e (radiation) and v (photometric). These quantities are listed in the following table, together with their radiometric equivalents to indicate the relation between the two systems of measurement.



Photometric quantities

Quantity

Radiometric equivalent

Symbol

Definition

Unit name and symbol

Luminous flux

     Radiant power

 

    lumen         lm

Luminous intensity

     Radiant intensity

I

/∂Ω

    candela      cd ≡ lm sr−1

Luminance

     Radiance

L

2/∂A ∂Ω

    (nit)            cd m−2

Illuminance

     Irradiance

E
M
/∂A

    lux              lm m−2

Luminous exitance

     Radiant exitance

                      lm m−2




Luminance and colour temperature of selected light sources

Light source

Luminance

104 cd m−2

Correlated color
temperature

K

     
Candle

1    

~ 2000   

Paraffin flame (flat wick)

1.25

2055

Acetylene flame (Kodak burner)

10.8   

2360

Tungsten strip lamp (vacuum)

124        

2400

Tungsten strip lamp (gas-filled) 540        

2800

Tungsten coil lamp (quartz-halogen)

~ 2800    

~ 3300   

Mercury vapour (low pressure, in gas)

2.3     

—   

      ,,      (high pressure, compact, 250 W)

20 000   

—   

      ,,      (medium pressure, metal halide, 400 W)

880       

4000

      ,,      (tabular fluorescent, warm white, 40 W)

1.9

3000

      ,,      (tabular fluorescent, triphosphor, 36 W)

3.5

3000

Sodium discharge (high pressure,150 W)

750      

2000

High intensity carbon arc

80 000  ~ 5000   

Xenon arc (continuous compact, 250 W)

25 000 

6000

Clear blue sky

~ 0.4    

12 000–24 000

Starlit sky

    ~ 5 × 10−8

—   
Zenith sun (through atmosphere)

   ~ 160 000

5400

Moon (through atmosphere)

~ 0.4    

—   
     



Scotopic system of photometry

At low levels of luminance the relative luminous effects of radiations of different wavelength are in general no longer represented even approximately by the values of V(λ) given in the above table. This is because a different visual mechanism known as the scotopic or dark-adapted mechanism, as opposed to the photopic or light-adapted mechanism, is dominant. To evaluate electromagnetic radiation with respect to the effect it produces on the scotopic mechanism, an alternative set of weighting factors—the scotopic spectral luminous efficiency function V'(λ)—must be used, the values of which were agreed by the CIE in 1951 and accepted by the CIPM in 1976.


Scotopic spectral luminous efficiency function V'(λ)

λ/nm

(λ)

λ/nm

(λ)

λ/nm

(λ)

λ/nm

(λ)

λ/nm

(λ)

                   

300

400

0.0093

500

0.9820

600

0.0332

700

—  

310

410

0.0348

510

0.9970

610

0.0159

710

—  

320

420

0.0966

520

0.9350

620

0.0074

720

—  

330

430

0.1998

530

0.8110

630

0.003  

730

—  

340

440

0.3281

540

0.6500

640

0.0015

740

—  

350

450

0.4550

550

0.4810

650

0.0007

750

—  

360

460

0.5670

560

0.3288

660

0.0003

760

—  

370

470

0.6760

570

0.2076

670

0.0001

770

—  

380

0.0006

480

0.7930

580

0.1212

680

0.0001

780

—  

390

0.0022

490

0.9040

590

0.0655

690

790

—  

                   

In the alternative system of photometry obtained by taking V′(λ) as basis instead of V(λ), all the formal definitions of the previous section are retained, with terms modified by the adjective ‘scotopic’ and symbols by the addition of a prime. The calculated value for the scotopic maximum luminous efficacy K'm is 1700.06 lmW−1, which may safely be rounded to 1700 lm W−1.

In the so-called mesopic region between the photopic and the scotopic, the concept of luminous flux as an additive quantity does not apply and there is at present no agreed method of spectral weighting for mesopic vision.




Reference

ISO/CIE 10527 (1991) CIE Standard Colorimetric Observers.

O.C.Jones / T.M.Goodman

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