Moon Brightness Calculator

Introduction

This tool allows to modelling the Moon sky brightness at any time and place. No source other than the Moon is considered (i.e. integrated starlight, sky background, airglow, etc).

A paper describing the model and the use of the tool is being prepared.

How to use it

Input modes

Moon data at a given time and place: the altitude above the horizon, illuminated fraction and distance are computed and used to get the Moon sky brightness.

Moon data: the Moon altitude above the horizon, illuminated fraction and distance can be set by the user, as well as the observer's height.

File upload: a file with the input data for a time sequence (GMT / UT) or different Moon data is used. The photometrtic band is taken from the web.

NOTE: Each single computation takes a few seconds. For a file with hundreds of lines, the total computing time could be very long. We recommend limiting the size of the input file to no more than one hundred lines, which should take a few minutes.

Output

Global Horizontal irradiance / illuminance: the total amount of radiation, per unit area, received from above by a horizontal surface:

with Δ_i the HealPix solid angle element (sr).

For the human photopic and scotopic bands, E is multiplied by 683 lm/W or 1700 lm/W, respectively, to get the corresponding Horizontal illuminances (lx).

Average upper hemisphere radiance / luminance: obtained by directly averaging the equal-solid angle HealPix radiance across the upper hemisphere. The same for the photopic and scotopic luminances, in cd·m^-2.

Average full sphere radiance / luminance: the average of the radiance / luminance calculated taking into account not only the upper hemisphere above the observer but also the light from the sky reflected by the ground (the 'lower hemisphere'). To simplify, we assume the ground reflects light in a Lambertial way, with the in-band terrain reflectance ρ.

Radiance / luminance at Zenith: average radiance / luminance of the circular sky region (radi=5°) around the zenith. For the SQM and TESS bands is the average radiance in the filed of view of the instrument, taken into account the angular response.

Posch ratio 1: Global Horizontal Irradiance / Radiance at Zenith

Posch ratio 2: Average Upper Hemisphere Radiance / Radiance at Zenith

Photometric bands

The web provides a set of available photometric bands (see below). The user can also use any photometric band by uploading a two-columns file with the wavelenght (nm) and the transmission [0,1].

The currently available photometric bands are

Johnson-Cousins system (UBVRI)

The UBVRI magnitudes are defined in the Vega system. The fluxes in those bands correspond to filters with transmission peak equal to 1.

Gaia filter (G)

The Gaia magnitude is defined in the Vega system. Note that the filter's transmission is not normalized to 1.

SQM and TESS-W bands

SQM and TESS-W bands are defined in the AB system. The fluxes in those bands correspond to filters with transmission peak equal to 1

RGB System

The RGB magnitudes are defined in the AB system. The fluxes in those bands correspond to filters with transmission peak equal to 1

Human vision (photopic and scotopic)

Photopic and scotopic magnitudes are defined in the Vega system. The fluxes in those bands correspond to filters with transmission peak equal to 1

Sloan system (ugriz)

The Sloan magnitudes are defined in the AB system. Note that the filter transmission are not normalized.