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Robert Luther Aus dem Gebiet der Farbreizmetrik (On color stimulus metrics) Zeitschrift für technische Physik 8 (1927) An English translation with a short biographical introduction by Rolf G. Kuehni

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Robert Luther Aus dem Gebiet der Farbreizmetrik (On color stimulus metrics) Zeitschrift für technische Physik 8 (1927) An English translation with a short biographical introduction by Rolf G. Kuehni and a technical introduction by Michael H. Brill Copyright statement: Copyright of original paper: unknown; copyright of translation and biographical introduction: Rolf G. Kuehni, 2009; copyright of technical introduction: Michael H. Brill, Note Explanatory wording by the translator in angular parentheses. There are three extended explanatory notes by the translator identified with alphabetical superscripts. 2 Robert Luther Dresden, ca U. Richter Robert (Thomas Diedrich) Luther was born in Moscow to German parents on Jan. 2, His father Alexander was a lawyer. Among his direct ancestors was Hans Luther ( ), a cousin of the reformer Martin Luther. From 1885 to 1889 he studied chemistry at the University of Dorpat in Russia. Toward the end of 1889 he was named assistant to the chemist F. K. Beilstein at the University of St. Petersburg. A serious illness in 1891 forced him to recuperate during the next two years. In 1894 he resumed studying chemistry, this time at the University of Leipzig where he received his PhD degree in His primary educator there was Wilhelm Ostwald ( ). In 1896 Luther was named an assistant to Ostwald at the Physico-Chemical Institute of the University of Leipzig. In 1899 Luther submitted his habilitation thesis, titled Equilibrium change between halogen compounds of silver and the free halogens caused by light, and obtained lecturer status. In the same year he published the monograph The chemical processes of photography, a record of six public lectures he gave on the subject. In these lectures he demonstrated, among many other things, the chemical reaction kinetics in layers or volumes of substances, a subject that occupied him for the rest of his life. He also was the co-author of the 1902 second edition of Ostwald s book on experimental methodology in physico-chemical measurements. In the year 1900 he was named assistant director of the Ostwald Institute at the University of Leipzig. As colleagues, Ostwald and Luther were considerably different types. Ostwald did not like to have to lecture but published many papers and books. As a result, Luther was burdened with much of the lecturing activities at Ostwald s institute. Despite important work in many fields he rarely wrote articles. In 1904 Luther was named a regular professor of physical chemistry at the University of Leipzig. Ostwald, wanting to just manage the Institute, was found to be neglecting his lecturing duties and resigned from his position in 1906, retreating to his country estate in Grossbothen, where he launched 3 into his color research. In the same year Luther was named director of the newly-formed photochemical department. In the fall-out of Ostwald s departure Luther found himself in a difficult position in Leipzig and in 1908 accepted an appointment at the Photographic Science Institute of the Technical University of Dresden, organized shortly before with the support of the local photographic industry (such as Zeiss). Luther remained there until his change to professor emeritus status in 1936, performing significant research in photographic and general physical chemistry and also concerning himself with the definition of color stimuli and color stimulus measurement. He was much admired by his students, among them Manfred Richter who later developed the DIN color order system. In the famous American photographer Imogen Cunningham ( ) was a student of Luther, learning the technique of platinum prints. Luther remained in Dresden where he passed away on April 17, 1945, the last day of the Allied bombing runs on that city. Luther s interest in color phenomena was the natural outcome of his activities related to the chemistry of color photography. He clearly distinguished between what he considered to be objective definition of color stimuli and perceptual color phenomena. Most of his seminal paper On color stimulus metrics, offered here in translation, was ready for publication in 1923 under the title Color and spectrum, as a contribution to a Festschrift for Ostwald in the Zeitschrift für angewandte Chemie. However, the rabid inflation of the time prevented publication until 1927, as described in Footnote 4 of the paper. His only other brief (2 pages) publication on the subject of color, from 1942, is concerned with practical application of the moment sum curve, developed in the 1927 paper. Sources of biographical information: 1. M. Richter, Robert Luther, Die Farbe 3: (1955). 2. A. Fischer, Luther, Robert, in: W. Pötsch (ed.) Lexikon bedeutender Chemiker, Frankfurt: Verlag Harry Deutsch, Technical Introduction The article translated here is a rare summary of thoughts on color by Robert Luther. The content is quite heterogeneous, because it represents an accumulation of ideas that could not find earlier publication during a period when Luther s Germany faced financial calamity. 1. General Outline The article has two main parts. The first part (Sections 1-19), written with the goal of much earlier publication, is mainly theoretical. In it we find an introduction to tristimulus space, the embedding therein of the object-color solid (given a pre-defined illuminant spectrum), and the optimal colors on the exterior surface of the object-color solid (comprising reflectances that at all visible wavelengths have values of either 0 or 1 with at most two transitions between them). Some of the optimal colors, called end colors, are those with only one transition. (Visualizing the optimal-color surface as a clamshell, the end colors are where the two halves of the shell join.) Other optimal colors, called full colors, comprise the curve on the object-color solid that would just touch the minimum cylinder that contains that solid and is parallel to the achromatic axis. (If the object-color solid were a key and the cylinder were a lock, the full colors would be the points on the key that brush the inside of the lock.) All these constructs, and others in Luther s article, emerge most immediately from the theoretical work of Wilhelm Ostwald, and also owe some debt to works such as those of Erwin Schrödinger and Hermann Helmholtz. But Luther offers some new contributions as well. For example, he was probably the first to draw the shape of the object-color solid, and did so in several coordinate systems. The second part (Sections 20-25) is a smorgasbord of material with a more practical flavor. In Section 20 we find a design of a template colorimeter and a discussion of filter colorimeters. Section 21 discusses a single-color sensor whose spectral sensitivity is compensated to the human luminosity sensitivity---a one-dimensional form of a tristimulus colorimeter or colorimetrically correct camera. Section 22 explains and endorses heterochromatic flicker photometry. Then Section 23 describes criteria for a trichromatic camera. Finally, Sections 24 and 25 wax philosophical about subjective versus objective colors: Luther saw subjective colors as illusions or perturbations on real physical colors---quite a contrast with more modern views. In Part 1 Luther adds to Ostwald s optimal colors a set of mathematical relations among the optimal colors in tristimulus space. Perhaps the restriction of that mathematics to optimal-color reflectances has limited its familiarity in the color-science community. Luther is credited, not for his optimal-color constructs, but for a rule for camerasensitivity functions---that they should be nonsingular linear combinations of human color-matching functions to make the same color matches we do. A question for historians is how this statement is an advance over the earlier statements by James Clerk Maxwell [2] and Frederic Ives [3]. 5 To give a flavor for and cast in modern terms some ideas in Luther s article, I choose one topic from Part I and one from Part II: I attempt to explain in modern terms the parallelchord theorem of Section 11, and examine Section 23 in its own right and as it bears on the camera-sensitivity rule called by some the Luther criterion. 2. An example from Part I: The parallel chord theorem In Section 11 Luther poses a theorem that relates equal dominant wavelength and parallel chords in a particular color space. The English translation says, The required wavelength range and the brightness of an optimal color can be read from the portion of the curved double scale located clockwise between the beginning and the end of the chord. A chord can be deconstructed into its two (vertical) primary moments, the ratio of which, according to absolute value and sign, indicates the direction and thereby the hue. Therefore, chords that, as vectors, are parallel represent optimal colors of the same hue. In context, it seems clear that by hue he means dominant wavelength. To me the proof needs much elaboration, so I offer it here. The key to understanding the theorem is through Figure 9, a two-dimensional space in which appears a curve with several chords drawn---ostensibly parallel to each other. Thanks to conversations with Jan Koenderink of Utrecht, NL, the space, the curves, and the chords became clear: a. The 2D space comprises two tristimulus dimensions---the exact choice doesn't matter, but black and white should be at the origin. As a geometric pictorial aid, you can imagine looking in parallel (not central) projection along the achromatic axis in 3D. b. The curve in Fig. 9 represents one of the two loci (curves) of end colors. Together the long-end and short-end loci form a figure-8 shape crossing at the achromatic point: Half of the 8 comprises the long-end colors (up-transition wavelength parameter λ 1 ), and the other half comprises the short-end colors (down-transition wavelength parameter λ 2 ). c. One might have expected a chord in Fig. 9 to connect one point from the λ 1 loop of the figure-8 and one point from the λ 2 loop. But Luther uses only one of the loops (e.g., the short-end-color loop), and finds both λ 1 and λ 2 on that loop. [One loop maps on the other (replete with wavelength labels) by a coordinate inversion.] d. Given the above, here is the theorem: Let two pass-band optimal colors have transition-wavelength pairs (λ 1, λ 2 ) and (μ 1, μ 2 ), where λ 1 λ 2 and μ 1 μ 2. Denoting the unit step function by u, the (λ 1, λ 2 ) optimal reflectance as a function of wavelength λ is u(λ - λ 1 ) - u(λ λ 2 ), and the (μ 1, μ 2 ) optimal reflectance is given by u(λ - μ 1 ) - u(λ μ 2 ). Integrating in λ with respect to the two illuminant-weighted color-matching functions, we get 2-vectors denoted by x: x(λ 1 ) - x(λ 2 ) and x(μ 1 )- x(μ 2 ). The various points x are the points on the short-end-color curve: x(λ 1 ), x(λ 2 ), x(μ 1 ), x(μ 2 ). The theorem is: If these two pass-band colors have the same dominant wavelength, the vectors x(λ 1 ) - x(λ 2 ) and x(μ 1 )- x(μ 2 )---which are the directions of the chords between the λ s and between the μ s---are parallel to each other. 6 e. A proof of the theorem: The dominant wavelength of a tristimulus vector X is the wavelength λ such that X(λ ), X, and W are coplanar (where W is the tristimulus vector of white). That means det[x(λ ), X, W] = 0. If two tristimulus vectors X L and X M have the same dominant wavelength, then they are coplanar with each other and with W: det[x L, X M, W] = 0. Now, we have chosen tristimulus coordinates so W is nonzero only in its third component. Therefore the above determinant equation is equivalent to 0 = det[x L, x M ], where x L and x M are the 2-vectors in the dichromatic space. Substituting x(λ 1 ) - x(λ 2 ) for x L and x(μ 1 )- x(μ 2 ) for x M, the zero-determinant condition implies that the vectors are linearly dependent, and hence (being in 2D) must be parallel. To me, the parallel chord theorem shows the originality of Luther s geometrical insight. However, because it deals only with optimal colors---which do not exist in nature---the theorem has not been widely used. It would be interesting to look in Luther s Part 1 for mathematical insights of more general applicability that have escaped modern attention. 3. An example from Part 2: Camera-sensitivity criterion Section 23, on color photography, contains remarks on the spectral sensitivities of an ideal camera, and also on filter spectra required for a color-accurate additive synthesis of three images from three color-separated negatives. I will focus here on his criteria for camera-sensitivity functions because they have received a lot of citation and attention. The roots of Luther s design of camera-sensitivity functions are to be found in the short paragraph that ends Section 20 and describes the design of a tristimulus colorimeter: [...] it is possible to use undispersed light with suitable selective filters. In that case it is of course necessary that the spectral transmittance of T λ of the filter, for example for the red stimulus determination, is in agreement with the following precondition: T λ E λ = R λ. Hence, the filter-detector combination ideally has the same sensitivity as a colormatching function R of the visual system. In Section 23, the design of the tristimulus colorimeter is transferred with very little fanfare to the spectral sensitivities of a color-faithful camera. The message is that, to make the same matches as the eye, the camera must have spectral sensitivities close to those of the eye. In the years that followed Luther s article, the principle he described evolved to a more precise form: In order for a trichromatic camera to match the same colors as the human observer, the spectral sensitivity functions of that camera must be linear combinations (and together must comprise a nonsingular linear transformation) of the human-observer color-matching functions. That criterion has variously been called the Maxwell-Ives criterion [4] and the Luther condition [5]. The term Luther-Bedingung was introduced by Manfred Richter [6], a student of Luther. 7 As brief as Luther s version of the camera-sensitivity criterion is, I will now make the case that it is an advance over the earlier versions by Maxwell and Ives. Maxwell s 1855 version appears on pages of [4]: Three elementary effects, according to [Young s] view, correspond to the sensations of red, green, and violet, and would separately convey to the sensorium the sensation of a red, a green, and a violet picture; so that by the superposition of these pictures, the actual variegated world is represented. [ ] This theory of colour may be illustrated by a supposed case taken from the art of photography. Let it be required to ascertain the colors of a landscape, by means of impressions taken on a preparation equally sensitive to rays of every colour. Let a plate of red glass be placed before the camera, and an impression taken. [ ] Let it now be put in a magic lantern, along with the red glass, and a red picture will be thrown on the screen. Let this operation be repeated with a green and a violet glass [ ] a complete copy of the landscape, as far as the visible color is concerned, will be thrown on the screen. The only apparent difference will be, that the copy will be more subdued, or less pure in tint, than the original. Here, however, we have performed the process twice---first on the screen, and then on the retina. This illustration will show how the functions which Young attributes to the three systems of nerves may be imitated by the optical apparatus. Maxwell clearly captured the imitation of color-matching functions by camera-sensitivity functions, and also recognized that the optical-projection part of the camera s function is separate and distinct, desaturating the rendered colors. However, he did not separate mathematically the light-sensing and projecting functions, nor did he capture the linear transformation idea of the mature camera-sensitivity criterion. Ives s version of the criterion emerges by piecemeal examination of [3]: p. 13: [The] new principle, first stated by me in a communication to this institute on November 21, 1888, is that of making sets of negatives by the action of light in proportion as they excite primary color sensations, and images or prints from such negatives with colors that represent primary color sensations. pp : [ ] The eye is only capable of three primary color sensations [ ] According to Clerk Maxwell, the orange spectrum rays excite the red sensation more strongly than the brightest red rays, but also excite the green sensation [etc]; Maxwell s diagram is a graphic representation of the result of careful photometric measurements of the effect of the spectrum upon these primary sensations. p. 15: The plates and screens [producing a photographic negative] are correct when they will secure negatives of the spectrum showing intensity curves substantially like the curves in Maxwell s diagram. 8 Ives clearly separated the sensing function of the camera from the rendering function, and attributed the imitation of visual sensitivity firmly to the former. The linear transformation idea was still not on the horizon. Given these earlier works, it is not far-fetched to consider Luther s contribution a further step toward the mature criterion: a mathematical equation, and a precise though brief discussion of the equation. The linear-transformation freedom, however, is still not acknowledged. Lest we consider that Luther missed an obvious point, it is instructive to see how later authors incorporated the linear-transformation freedom. That property was clearly understood by Neugebauer in 1956 [7]. But consider MacAdam s 1967 work [4]: p. 28: Maxwell was quite specific about the required character of the controls. He said that three photographs should be made with spectral sensitivities proportional to the three spectral sensitivities had shown can be attributed to the eye to account for all of the infinite varieties of spectral distributions that can look alike (that is, have the same color ). In the next paragraph: Thirty years later, Frederic Ives had much more suitable materials, and also the single-minded persistence required to carry out Maxwell s idea and to demonstrate its validity to a skeptical and even hostile audience. But his success has little influence on the development of modern color photography. Through his son Herbert, however, it had a significant influence on the modern technology of color measurement that very effectively supplements spectroscopy (spectrophotometry) in all industries that supply colored products. Although MacAdam s words are accurate, the statement proportional to the three spectral sensitivities leaves unexpressed the freedom of linear transformation. It is a subtlety that gained significant attention only when computers became commonly available to exercise the linear transformation freedom. I found it quite educational to examine in this way the contribution of Maxwell, Ives, and Luther of the camera criterion that bears various combinations of their names. The earliest inventors of an idea did not necessarily grasp or express its complete essence. There may even be a fragment today that we are not using to complete advantage. 4. Conclusions This introduction has been a whirlwind tour of Luther s article followed by two highly focused micro-views. It cannot be said that I have stolen the thunder of the article or given away the ending. Luther s article is the work of a scholar of great accomplishment but terse expression, who has summarized color science as of the third decade of the 20 th Century in one diverse essay. Enjoy! Michael H. Brill Datacolor 9 [1] R. Luther, Aus dem Gebiet der Farbreizmetrik, Z. Technische Physik., 8, (1927). [English translation by Rolf G. Kuehni, 2009]. [2] J. C. Maxwell, Experiments on Colour as perceived by the eye with remarks

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