Shedding light on 19th century spectra by analyzing Lippmann photography Gilles Baechlera,1 , Arnaud Lattya, Michalina Pacholskaa , Martin Vetterlia , and Adam Scholefielda,1 aSchool of Computer and Communication Sciences, Ecole Polytechnique Fed´ erale´ de Lausanne, CH-1015 Lausanne, Switzerland Edited by David L. Donoho, Stanford University, Stanford, CA, and approved January 26, 2021 (received for review May 11, 2020) From uncovering the structure of the atom to the nature of the standard camera optics. As shown in Fig. 2, the photographic universe, spectral measurements have helped some of science’s plate consists of a light-sensitive emulsion on a sheet of glass. greatest discoveries. While pointwise spectral measurements date In addition, during exposure, a mirror is created at the emulsion back to Newton, it is commonly thought that hyperspectral surface, traditionally by putting the emulsion in contact with liq- images originated in the 1970s. However, the first hyperspec- uid mercury. For the image acquisition, the plate is orientated tral images are over a century old and are locked in the safes such that the light from the scene passes through the glass and of a handful of museums. These hidden treasures are exam- then the emulsion, before reflecting back from the mirror. This ples of the first color photographs and earned their inven- causes the light to interfere and the resulting interference pat- tor, Gabriel Lippmann, the 1908 Nobel Prize in Physics. Since tern exposes the emulsion differently at different depths. For the original work of Lippmann, the process has been predom- example, in the simple case of monochromatic light—that is, light inately understood from the monochromatic perspective, with made of a single wavelength—sinusoidal standing waves appear, analogies drawn to Bragg gratings, and the polychromatic case effectively creating a Bragg grating inside the photographic treated as a simple extension. As a consequence, there are emulsion. misconceptions about the invertibility of the Lippmann pro- From a chemical point of view (2), the exposure to light cess. We show that the multispectral image reflected from a neutralizes some of the silver halide ions from crystal grains dis- Lippmann plate contains distortions that are not explained by tributed throughout the emulsion. The reduced silver atoms form current models. We describe these distortions by directly model- tiny metallic specks whose aggregate is called a latent image. ing the process for general spectra and devise an algorithm to Since silver salts are sensitive only to blue and violet light, dyes recover the original spectra. This results in a complete analysis are added to the emulsion to extend the sensitivity across the full APPLIED MATHEMATICS of the Lippmann process. Finally, we demonstrate the accuracy visible spectrum. In Fig. 2, we assume that the dyes are tuned of our recovery algorithm on self-made Lippmann plates, for to make the plate isochromatic—that is, equally sensitive to all which the acquisition setup is fully understood. However, we wavelengths. show that, in the case of historical plates, there are too many Once the plate has been exposed, it is removed from the liquid unknowns to reliably recover 19th century spectra of natural mercury and processed via standard photographic development scenes. techniques. The development is a chemical reaction that com- pletes the reduction of silver halide into metallic silver in the Lippmann j photography j interference j spectrography exposed grains. The latent image serves as a catalyst for this reaction and thus the processed plate contains an enhanced ver- sion of the latent image. However, the enhancement is not a t is often claimed that the prevalence of air travel has made constant scaling of the latent image and depends on a num- Ithe sky less blue (1). To understand whether this is true or ber of characteristics of the process. For example, the developer just indulgent reminiscing, it seems natural to turn to the photo- graphic record. While modern multispectral cameras can provide extremely accurate color information with hundreds of spectral Significance samples taken in the visible range, most photographic techniques take just three measurements, for red, green, and blue. How- Gabriel Lippmann won the 1908 Nobel Prize in Physics for his ever, looking at the history of color photography, one early method of reproducing colors in photography. Despite the sig- technique stands out in terms of color reproduction: Lippmann nificance of this result, there are still misconceptions regarding photography. While this technique is analogue, we show that it the approach. We provide a complete end-to-end analysis of typically captures 26 to 64 spectral samples of information in the process and show, both theoretically and experimentally, the visible region, making it the earliest multispectral imaging how the spectrum reflected from a Lippmann plate is not technique. the same as the exposing spectrum. In addition, we demon- Although the technique provides the foundations of hologra- strate that, given the spectrum reflected from a Lippmann phy and much of modern interferometric imaging, it has been plate, together with the plate’s color absorption proper- almost completely forgotten today. In addition, as a photogra- ties, the original exposing spectrum can be algorithmically phy technique, it failed to achieve mainstream adoption, mainly recovered. due to excessively long exposure times and the impossibility to Author contributions: G.B., M.V., and A.S. designed research; G.B., A.L., M.P., and A.S. create copies. performed research; G.B. and A.L. contributed new reagents/analytic tools; G.B. and M.P. Fig. 1 shows digital images of an original Lippmann plate; one analyzed data; and G.B., A.L., M.P., M.V., and A.S. wrote the paper.y characteristic of these fascinating artworks is that the correct The authors declare no competing interest.y colors appear only under proper viewing conditions. Of course, This article is a PNAS Direct Submission.y static images do not do justice to these works and we strongly This open access article is distributed under Creative Commons Attribution-NonCommercial- recommend that readers view a real plate, if they ever have the NoDerivatives License 4.0 (CC BY-NC-ND).y opportunity. In addition, we provide a video of a Lippmann plate 1 To whom correspondence may be addressed. Email: [email protected] or under a moving light source, in Movie S1. adam.scholefield@epfl.ch. y Lippmann’s process works by capturing an interference pat- This article contains supporting information online at https://www.pnas.org/lookup/suppl/ tern in a photosensitive emulsion. More precisely, during expo- doi:10.1073/pnas.2008819118/-/DCSupplemental.y sure, the image is focused onto a photographic plate using Published April 15, 2021. PNAS 2021 Vol. 118 No. 17 e2008819118 https://doi.org/10.1073/pnas.2008819118 j 1 of 7 Downloaded by guest on October 2, 2021 AB r = ρ exp(j θ). Here, ρ is the attenuation factor and θ is the phase shift. As we will show, the choice of reflective medium plays a sig- nificant role in the color reproduction. The latent image—that is, the silver density after exposure—is proportional to the power of the superposed waves inside the emulsion:∗ Z 1 !z !z 2 2 L(z) / jA(!)j exp j + r exp −j d! 0 c c Z 1 2!z = jA(!)j2 1 + ρ2 + 2ρ cos − θ d!: 0 c Here, we have assumed that, as depicted in Fig. 2, the reflected wave travels in the positive z direction and z = 0 at the mirror. Development. As previously described and depicted in Fig. 2C, the development enhances the silver density of the latent image Fig. 1. Self-portrait of Gabriel Lippmann viewed under different illumina- differently at different depths. This can be modeled by a mul- tion. (A) Diffuse illumination. (B) Directed light whose incoming direction is tiplicative function W (z). This results in the following analysis the mirror image of the viewing direction with respect to the plate’s surface. operator, A, that maps the incoming power spectrum P(!) = jA(!)j2 to the developed silver density in the emulsion: solution diffuses from the top surface of the emulsion toward Z 1 2!z AfPg(z) = W (z) P(!) 1 + ρ2 + 2ρ cos − θ d!: the emulsion–glass interface, leading to a weaker development c at deeper depths. This explains the decaying nature of the silver 0 density in Fig. 2C. Here, we have incorporated the unknown proportionality factor Fig. 2 also shows that, before viewing, the plate is turned between the latent image and the power of the superposed waves upside down with respect to the orientation used for exposure into W (z). In addition, W (z) = 0 when z is outside the finite and the glass surface is painted black. In addition, a prism is thickness of the emulsion and, due to the diffusion described attached to the emulsion surface with an index-matched glue— previously, it decreases with increasing depth. historically, Canada balsam was the adhesive of choice. To view the captured image, the plate is illuminated with a white light Viewing. The recorded silver density pattern can be thought of source. The prism separates the front surface reflection from as elementary partially reflective mirrors, whose reflectance is the desired emulsion reflection and the black surface mini- proportional to the silver density after processing. When the mizes unwanted back reflections. The desired reflection from developed plate is illuminated, the light reflected from the emul- the emulsion consists of scattered light from the silver particles sion can be modeled as the sum of the reflections from each of distributed throughout the depth of the emulsion; depending these elementary partially reflective mirrors. This Born approx- on the wavelength, the reflected light waves add more or less imation neglects all but first-order reflections.