Shedding light on 19th century spectra by analyzing Lippmann photography

Abstract

From uncovering the structure of the atom to the nature of the universe, spectral measurements have helped some of science’s greatest discoveries. While pointwise spectral measurements date back to Newton, it is commonly thought that hyperspectral images originated in the 1970s. However, the first hyperspectral images are over a century old and are locked in the safes of a handful of museums. These hidden treasures are examples of the first color photographs and earned their inventor, Gabriel Lippmann, the 1908 Nobel Prize in Physics. Since the original work of Lippmann, the process has been predominately understood from the monochromatic perspective, with analogies drawn to Bragg gratings, and the polychromatic case treated as a simple extension. As a consequence, there are misconceptions about the invertibility of the Lippmann process. We show that the multispectral image reflected from a Lippmann plate contains distortions that are not explained by current models. We describe these distortions by directly modeling the process for general spectra and devise an algorithm to recover the original spectra. This results in a complete analysis of the Lippmann process. Finally, we demonstrate the accuracy of our recovery algorithm on self-made Lippmann plates, for which the acquisition setup is fully understood. However, we show that, in the case of historical plates, there are too many unknowns to reliably recover 19th century spectra of natural scenes.

Lippmann Photography: A Signal Processing Perspective

“…More details on the parameters' estimation are also provided in [9], where an algorithm is proposed to estimate the original spectrum, jointly with the thickness and the development decay. Using this algorithm, we showed in [1] that if the sensitivity of the recording medium is available, the original spectrum can be recovered with acceptable precision, which further confirms the validity of our model.…”

“…To perform a quantitative analysis of our model, one would need to measure additional parameters. It is possible to estimate some of them; for example, in [1] we have estimated the plate thickness Z from both spectrometric and electron microscopic measurements (Fig. 5B), which resulted in agreement within 10 %.…”

“…In recent work [1], we have shown that for polychromatic spectra, the reflected spectrum is not exactly the same as the recorded spectra. We proposed a mathematical model of the Lippmann plates.…”

“…In fact, Lippmann himself made such a claim in his 1894 paper using the premises of Fourier analysis [4]: "en d'autres termes, la couleur de l'image est la même que celle de l'objet." 1 More recently, H. Bjelkhagen, an expert in Lippmann photography and holography, wrote [5]: "The light is reflected from these fringes, creating precisely the colors that correspond to the original ones that had produced them during the recording. "…”

“…In this work, we derive and explain our model in more detail as well as verify experimentally the predicted distortions. Here, we take a signal processing view of the Lippmann process, whereas [1] is aimed at more general audience and hence lacks mathematical detail. In Section II we describe and model mathematically all three stages of the Lippmann process: recording, development and viewing.…”