Historical Context: The Controversy Over the Nature of Light
In the early 19th century, several experiments, including those by Thomas Young and Augustin-Jean Fresnel, led to the triumph of the wave theory of light. But not all scientists were convinced. Siméon Denis Poisson, a proponent of Isaac Newton’s corpuscular theory of light, was staunchly opposed to it. The controversy intensified with a question put forward by the Academy of Sciences in 1818. Poisson had noted on that occasion that one of the consequences of Fresnel’s wave theory would be the presence of a bright spot at the center of the shadow cast by a circular opaque disk, due to constructive interference of the wave. This seemed absurd to him: how could light illuminate the center of a completely black shadow? Especially since no one had ever observed such a spot… However, François Arago was able to produce one using a small metal disk. The jury members were convinced, and the Academy’s prize was awarded to Fresnel in 1819.
The Poisson spot: a phenomenon of light interference
In memory of these debates, the observed spot is now called the Poisson spot, or the Poisson-Arago spot, or the Fresnel spot. It made an unexpected reappearance during calculations performed to describe the “central flashes” observed during stellar occultations by objects such as Pluto or Triton (figure opposite). The question was: what is the structure of the flash produced by a perfectly spherical and transparent atmosphere? Can its amplitude be infinite? What is the role of diffraction?
Application to stellar occultations by Pluto and Triton
The calculations describing the flash involve path integrals and use Sommerfeld’s lemma, which is essential in quantum mechanics. A logical situation: photons are, by definition, quantum objects! From there, the authors consider several scenarios, starting with a spherical occulter without an atmosphere and of radius R0, and a star assumed to be point-like. This yields the classical Poisson spot, whose maximum irradiance is equal to that received from the star outside the shadow. The Poisson spot is described by the square of the Bessel function of the first kind and zero order, J0. It is an oscillating function that reaches unity at the center of the shadow and has a width close to λ∆/(2R0), where λ is the observation wavelength and ∆ is the geocentric distance of the occulting body. This peak is also surrounded by fringes, equally spaced at approximately λ∆/(2R0).
If a thin atmosphere is introduced—but one that is too weak to focus the light rays toward the center of the shadow—not only does the Poisson spot persist, but it is amplified by a factor of (R0/r0) 2, where r0 < R0 is the radius of the shadow cast by the body, taking into account the refraction of light rays due to the atmosphere of the occluder. The figure opposite shows the theoretical structure of the shadow of Pluto, whose atmospheric pressure has been arbitrarily reduced to one-tenth of its current value, as observed in millimeter waves. The Fresnel fringes mentioned above can be seen at the edges of the shadow, as well as the central Poisson spot amplified by a factor of (R0/r0)².
“If the atmosphere is dense enough to focus the light rays toward the center of the shadow, r0 no longer exists. Calculations then show that diffraction imposes a finite flash height of approximately (2π)²RH/(λΔ), where R is the radius of the layer causing the central flash (close to R₀), and H is the height scale of the atmosphere. For Pluto and Triton (with 0.01 mbar at the surface), this flash height can reach very large values in the visible spectrum, ranging from 10⁴ to 10⁵ times the star’s luminance outside of occultation. At the same time, the width of the flash projected onto Earth, λ∆/(2R), is extremely small, on the order of a meter, making its resolution impossible with current technology. However, since this width is proportional to λ, observations made at millimeter wavelengths could resolve the flash and the fringes surrounding it, which would then have sizes on the order of a kilometer.”
The Influence of Finite Stellar Size and Atmospheric Distortions on the Modeling of Central Flashes
That said, other effects must be taken into account to describe the flash. For example, the size of the occulted star is finite. When projected onto the occulting plane, this size is typically on the order of a kilometer. This implies that diffraction effects are smoothed by the stellar diameter: in the case of a thin atmosphere, the height of the central flash is then less than (R0/r0)²; in the case of a dense atmosphere like Pluto’s current one, calculations show that despite this smoothing, the flash can still reach heights more than 50 times the star’s initial signal. Another effect to consider is the possible distortion of the atmosphere relative to the spherical model. In this case, the Poisson spot is replaced by a caustic surrounded by fringes, a topic for future study…
Reference
The article was published under the title: “Central flashes during stellar occultations.
Effects of diffraction, interference, and stellar diameter” on March 17, 2026, https://doi.org/10.1051/0004-6361/202555548
This research is the result of scientific activities conducted in France at the Paris Observatory - PSL’s Time and Space Laboratory (Paris Observatory – PSL / CNRS / Sorbonne University / University of Lille) and at Jean Monnet University Saint-Étienne, CNRS, Institut d’Optique Graduate School, Hubert Curien Laboratory, UMR 5516.