Fundamental concepts of photometry

Figure 2.9: Spectral luminous efficiency function of the “standard” light-adapted eye for photopic visionV (λ)and scotopic visionV(λ), respectively.

withλ1=0andλ2= ∞as a special case. All definitions and relations derived in Sections2.3.3and2.3.4can be used for both spectral distri-butions of radiometric quantities and total quantities, integrated over the spectral distribution.

2.4 Fundamental concepts of photometry

Photometryrelates radiometric quantities to the brightness sensation of the human eye. Historically, the naked eye was the first device to measure light, and visual perception remains important for design-ing illumination systems and computdesign-ing the apparent brightness of sources and illuminated surfaces.

While radiometry deals with electromagnetic radiation of all wave-lengths, photometry deals only with the visible portion of the electro-magnetic spectrum. The human eye is sensitive to radiation between 380and 780nm and only radiation within this visible portion of the spectrum is called “light.”

2.4.1 Spectral response of the human eye

Light is perceived by stimulating the retina after passing the preretinal optics of the eye. The retina consists of two different types of receptors:

rods and cones. At high levels of irradiance the cones are used to detect light and to produce the sensation of colors (photopic vision). Rods are used mainly for night vision at low illumination levels (scotopic vision).

Both types of receptors have different sensitivities to light at different wavelengths.

The response of the “standard” light-adapted eye is defined by the normalizedphotopic spectral luminous efficiency functionV(λ)(Fig.2.9).

It accounts for eye response variation as related to wavelength and

shows the effectiveness of each wavelength in evoking a brightness sen-sation. Correspondingly, thescotopic luminous efficiency functionV(λ) defines the spectral response of a dark-adapted human eye (Fig.2.9).

These curves were formally adopted as standards by the International Lighting Commission (CIE) in 1924 and 1951, respectively. Tabulated values can be found in [1,2,3,4,5]. Both curves are similar in shape.

The peak of the relative spectral luminous efficiency curve for scotopic vision is shifted to 507 nm compared to the peak at 555 nm for photopic vision. The two efficiency functions can be thought of as the transfer function of a filter, which approximates the behavior of the human eye under good and bad lighting conditions, respectively.

As the response of the human eye to radiation depends on a variety of physiological parameters, differing for individual human observers, the spectral luminous efficiency function can correspond only to an average normalized observer. Additional uncertainty arises from the fact that at intermediate illumination levels both photopic and scotopic vision are involved. This range is calledmesopic vision.

2.4.2 Definition of photometric quantities

In order to convert radiometric quantities to their photometric counter-parts, absolute values of the spectral luminous efficiency function are needed instead of relative functions. The relative spectral luminous efficiency functions for photopic and scotopic vision are normalized to their peak values, which constitute the quantitative conversion fac-tors. These values have been repeatedly revised and currently (since 1980) are assigned the values 683 lm W⁻¹ (lumen/watt) at 555 nm for photopic vision, and 1754 lm W⁻¹ at 507 nm for scotopic vision, re-spectively. The absolute values of the conversion factors are arbitrary numbers based on the definition of the unitcandela (or international standard candle) as one of the seven base units of the metric system (SI) [6,7].

The conversion from photometric to radiometric quantities reduces to one simple equation. Given the conversion factors for photopic and scotopic vision, any (energy-derived) radiometric quantityQe,λ can be converted into its photometric counterpartQν by

Qν =683 lm W⁻¹

780

380

Qe,λV(λ)dλ (2.27)

for photopic vision and

Qν =1754 lm W⁻¹

780

380

Qe,λV(λ)dλ (2.28)

2.4 Fundamental concepts of photometry 29 for scotopic vision, respectively. From this definition it can be con-cluded that photometric quantities can be derived only from known spectral distributions of the corresponding radiometric quantities. For invisible sources emitting radiation below 380nm or above 780nm all photometric quantities are null.

Table2.2summarizes all basic photometric quantities together with their definition and units.

Luminous energy and luminous flux. The luminous energy can be thought of as the portion of radiant energy causing a visual sensation at the human retina. Radiant energy beyond the visible portion of the spectrum can also be absorbed by the retina, maybe causing severe damage to the tissue, but without being visible to the human eye.

Theluminous flux defines the total luminous energy per unit time interval (“luminous power”) emitted from a source or received by a de-tector. The units for luminous flux and luminous energy are lm (lumen) and lm s, respectively.

Luminous exitance and illuminance. Corresponding to radiant exi-tance and irradiance, the photometric quantitiesluminous exitanceand illuminancedefine the luminous flux per unit surface area leaving a surface or incident on a surface, respectively. As with the radiometric quantities, they are integrated over the angular distribution of light.

The units of both luminous exitance and illuminance are lm m⁻²or lux.

Luminous intensity. Luminous intensity defines the total luminous flux emitted into unit solid angle under a specified direction. As with its radiometric counterpart, radiant intensity, it is used mainly to describe point sources and rays of light. Luminous intensity has the unit lm sr⁻¹ or candela (cd). For a monochromatic radiation source withIλ = I0δ(λ−555 nm)andI0 = 1/683 W sr⁻¹, Eq. (2.27) yieldsIν = 1 cd in correspondence to the definition of candela.

Luminance. Luminancedescribes the subjective perception of “bright-ness” because the output of a photometer is proportional to the lumi-nance of the measured radiation (Chapter4). It is defined as luminant flux per unit solid angle per unit projected surface area perpendicular to the specified direction, corresponding to radiance, its radiometric equivalent.

Luminance is the most versatile photometric quantity, as all other quantities can be derived by integrating the luminance over solid angles or surface areas. Luminance has the unit cd m⁻².

2.4.3 Luminous efficacy

Luminous efficacy is used to determine the effectiveness of radiative or electrical power in producing visible light. The term “efficacy” must not be confused with “efficiency.” Efficiency is a dimensionless constant describing the ratio of some energy input to energy output. Luminous efficacy is not dimensionless and defines the fraction of luminous en-ergy output able to stimulate the human visual system with respect to incoming radiation or electrical power. It is an important quantity for the design of illumination systems.

Radiation luminous efficacy. Radiation luminous efficacyKr is a mea-sure of the effectiveness of incident radiation in stimulating the percep-tion of light in the human eye. It is defined as the ratio of any photo-metric quantityQν to the radiometric counterpartQe integrated over the entire spectrum of electromagnetic radiation:

Kr =Qν

Qe [lm W⁻¹], where Qe= ∞ 0

Qe,λdλ (2.29) It is important to note that Eq. (2.29) can be evaluated for any radiomet-ric quantity with the same result forKr. SubstitutingQν in Eq. (2.29) by Eq. (2.27) and replacingQe,λby monochromatic radiation at 555 nm, that is,Qe,λ =Q0δ(λ−555 nm),Kr reaches the value 683 lm W⁻¹. It can be easily verified that this is the theoretical maximum luminous efficacy a beam can have. Any invisible radiation, such as infrared or ultraviolet radiation, has zero luminous efficacy.

Lighting system luminous efficacy. Thelighting system luminous ef-ficacyKsof a light source is defined as the ratio of perceptible luminous fluxΦν to the total powerPesupplied to the light source:

Ks=Φν

Pe [lm W⁻¹] (2.30) With theradiant efficiencyη˜=Φe/Pedefining the ratio of total radiative flux output of an illumination source to the supply power, Eq. (2.30) can be expressed by the radiation luminous efficacy,Kr:

Ks=Φν

Φe

Φe

Pe =Krη˜ (2.31)

Because the radiant efficiency of an illumination source is always smaller than 1, the lighting system luminous efficacy is always smaller than the radiation luminous efficacy. An extreme example is monochromatic laser light at a wavelength of 555 nm. AlthoughKr reaches the max-imum value of 683 lm W⁻¹,Ks might be as low as 1 lm W⁻¹ due to the low efficiency of laser radiation.