The troland (symbol Td), named after Leonard T. Troland, is a unit of ''conventional retinal illuminance''. It is meant as a method for correcting photometric measurements of

luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls wit ...

values impinging on the

human eye The human eye is a sensory organ in the visual system that reacts to light, visible light allowing eyesight. Other functions include maintaining the circadian rhythm, and Balance (ability), keeping balance. The eye can be considered as a living ...

by scaling them by the effective

pupil The pupil is a hole located in the center of the iris of the eye that allows light to strike the retina.Cassin, B. and Solomon, S. (1990) ''Dictionary of Eye Terminology''. Gainesville, Florida: Triad Publishing Company. It appears black becau ...

size. It is equal to retinal illuminance produced by a surface whose luminance is one nit when the apparent area of the entrance pupil of the eye is 1 square millimeter. The troland unit was proposed in 1916 by Leonard T. Troland, who called it a photon. The troland typically refers to the ordinary or

photopic Photopic vision is the vision of the eye under well-lit conditions (luminance levels from 10 to 108 cd/m2). In humans and many other animals, photopic vision allows color perception, mediated by cone cells, and a significantly higher vis ...

troland, which is defined in terms of the photopic luminance: :

T = L \times p ,

where ''L'' is the photopic luminance in cd⋅ m⁻² and ''p'' is pupil area in mm². A scotopic troland is also sometimes defined: :

T' = L' \times p ,

where ''L''′ is the scotopic luminance in cd⋅ m⁻² and ''p'' is pupil area in mm². Although named "retinal illuminance" (and originally named "photon" by Troland), trolands do not measure the actual photon flux incident on the retina; that quantity depends on the specific wavelengths of light that constitute the luminance used in the calculation.

Units conversion

Troland does not directly convert to other units, being a retinal luminance per unit area of a pupil. However Troland is linked to retinal illuminance in as follows. Assuming the corneal luminance ''L'' from an extended source, the pupil diameter ''p'' and the focal length of the eye ''F'', the retinal luminance is: : ''L''r m/m²= ''π'' ⋅ ''L'' / 4 / (''f''/#)² ≈ ''π'' ⋅ ''L'' ⋅ ''p''² / 4 / ''F''². Multiplying by the pupil area: Trolands d/m² ⋅ mm²= ''L'' ⋅ ''π'' ⋅ ''p''²/4 = ''F''² ⋅ ''L''_r ≈ 289 ⋅ ''L''_r. Alternatively, the retinal illuminance ''L''_r m/m²= Trolands / 289 m² As provided by a more accurate optical calculations, the conversion factor is 278 rather than 289 as demonstrated by simplified considerations above. Sometimes (by convention only, although not rigorously accurate by definition), retinal luminance is expressed in d/m²= m/sr/m² Assuming a Lambertian surface, 1 cd/m² = ''π'' lm/m² = ''π'' lux. That is, 1 d/m²= 289/''π''

roland Roland (; ; or ''Rotholandus''; or ''Rolando''; died 15 August 778) was a Frankish military leader under Charlemagne who became one of the principal figures in the literary cycle known as the Matter of France. The historical Roland was mil ...

≈ 92

Physical quantities

* luminance * equivalent luminancewolframalpha.com
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Unit system

centimeter–gram–second (CGS)

Basic unit dimensions

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Comparisons

* ≈ 0.8 × luminance of a kerosene candle (≈ 12000 cd/m² ) * ≈ luminance of a sperm candle (≈ 10000 cd/m² ) * ≈ luminance of an average daytime clear sky (≈ 8000 cd/m²)

References