Photometrie, sive de mensura et gradibus luminis, colorum et umbrae, better known as Photometria, is a book on the measurement of light by Johann Heinrich Lambert published in 1760. It established a complete system of photometric quantities and principles; using them to measure the optical properties of materials, quantify aspects of vision, and calculate illumination.
Content Written in Latin, the title of the book is a word Lambert devised from Ancient Greek: φῶς, φωτος (transliterated phôs, photos) = light, and μετρια (transliterated metria) = measure. Lambert’s word has found its way into European languages as photometry, photometrie, and fotometria. Photometria was the first work to accurately identify most fundamental photometric concepts, assemble them into a coherent system of photometric quantities, define these quantities with a precision sufficient for mathematical statements, and build from them a system of photometric principles. These concepts, quantities, and principles are still in use today. Lambert began with two simple axioms: light travels in a straight line in a uniform medium and rays that cross do not interact. Like Johannes Kepler before him, he recognized that "laws" of photometry are simply consequences and follow directly from these two assumptions. In this way Photometria demonstrated (rather than assumed) that
Illuminance varies inversely as the square of the distance from a point source of light, Illuminance on a surface varies as the cosine of the incidence angle measured from the surface perpendicular, and Light decays exponentially in an absorbing medium. In addition, Lambert postulated a surface that emits light (either as a source or by reflection) in a way such that the density of emitted light (luminous intensity) varies as the cosine of the angle measured from the surface perpendicular. In the case of a reflecting surface, this form of emission is assumed to be the case, regardless of the light's incident direction. Such surfaces are now referred to as "Perfectly Diffuse" or "Lambertian". See: Lambertian reflectance, Lambertian emitter. Lambert demonstrated these principles in the only way available at the time: by contriving often ingenious optical arrangements that could make two immediately adjacent luminous fields appear equally bright (something that could only be determined by visual observation) when two physical quantities that produced the two fields were unequal by some specific amount (things that could be directly measured, such as angle or distance). In this way, Lambert quantified purely visual properties (such as luminous power, illumination, transparency, reflectivity) by relating them to physical parameters (such as distance, angle, radiant power, and color). Today, this is known as "visual photometry." Lambert was among the first to accompany experimental measurements with estimates of uncertainties based on a theory of errors and what he experimentally determined as the limits of visual assessment. Although previous workers had pronounced photometric laws 1 and 3, Lambert established the second and added the concept of perfectly diffuse surfaces. But more importantly, as Ernst Anding pointed out in his German translation of Photometria, "Lambert had incomparably clearer ideas about photometry" and with them established a complete system of photometric quantities. Based on the three laws of photometry and the supposition of perfectly diffuse surfaces, Photometria developed and demonstrated the following:
1. Just noticeable differences In the first section of Photometria, Lambert established and demonstrated the laws of photometry. He did this with visual photometry and to establish the uncertainties involved, described its approximate limits by determining how small a brightness difference the visual system could determine. 2. Reflectance and transmittance of glass and other common materials Using visual photometry, Lambert presented the results of many experimental determinations of specular and diffuse reflectance, as well as the transmittance of panes of glass and lenses. Among the most ingenious experiments he conducted was to determine the reflectance of the interior surface of a pane of glass. 3. Luminous radiative transfer between surfaces Assuming diffuse surfaces and the three laws of photometry, Lambert used Calculus to find the transfer of light between surfaces of various sizes, shapes, and orientations. He originated the concept of the per-unit transfer of flux between surfaces and in Photometria showed the closed form for many double, triple, and quadruple integrals which gave the equations for many different geometric arrangements of surfaces. Today, these fundamental quantities are called View Factors, Shape Factors, or Configuration Factors and are used in radiative heat transfer and in computer graphics. 4. Brightness and pupil size Lambert measured his own pupil diameter by viewing it in a mirror. He measured the change in diameter as he viewed a larger or smaller part of a candle flame. This is the first known attempt to quantify pupillary light reflex. 5. Atmospheric refraction and absorption Using the laws of photometry and a great deal of geometry, Lambert calculated the times and depths of twilight. 6. Astronomic photometry Assuming that the planets had diffusely reflective surfaces, Lambert attempted to determine the amount of their reflectance, given their relative brightness and known distance from the sun. A century later, Zöllner studied Photometria and picked up where Lambert left off, and initiated the field of astrophysics. 7. Demonstration of additive color mixing and colorimetry Lambert was the first to record the results of additive color mixing. By simultaneous transmission and reflection from a pane of glass, he superimposed the images of two different colored patches of paper and noted the resulting additive color. 8. Daylighting calculations Assuming the sky was a luminous dome, Lambert calculated the illumination by skylight through a window, and the light occluded and interreflected by walls and partitions.
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