luox (RRID: SCR_020994) is implemented in JavaScript, HTML & CSS using React and chart.js. The source code is available under the GPL-3.0 License at GitHub ⁵⁶ . luox is deployed at https://luox.app/. Further details on implementation are given on the about page.

luox can be accessed online using any contemporary browser. The operational workflow is shown in Figure 1. The user measures an irradiance or radiance spectrum using their spectroradiometer and stores the spectrum in a CSV file. This file is then uploaded into the platform, which performs a series of calculations (detailed below) and visualises the spectrum in a report. This report can then be viewed in the browser, but also downloaded as a CSV file for sharing, e.g. as supplementary CSV file. The platform also allows for downloading the spectrum again as a CSV file. In addition, luox generates a shareable URL, which encodes the uploaded spectra in a URL (see below). A DOI can be requested which redirects to the shareable URL. The graphical user face is shown in Figure 2.

The luox platform includes a wizard, which details the requirements for files and expected file formats, and also includes a sample file containing three CIE Illuminants in the F series in 5 nm spacing. Upon uploading the file, calculations are performed, giving access to the workflow described above and in Figure 1.

The platform implements as a set of photometric, colorimetric, colour rendition and α-opic calculations based on a user-supplied irradiance [W/m ²/nm] or radiance [W/m ²/sr/nm] spectral power distribution S( λ). It is assumed that the user has

Photometry. luox implements the following photometric calculations:

•   Illuminance [lux] or luminance [cd/m ²]. Illuminance (for irradiance spectra) and luminance (for radiance spectra) corresponds to the spectrum weighted by the photopic luminosity function, V( λ), and multiplied by the constant 683 lm/W. V( λ) is based on psychophysical measurements (for a review, see 57) and was first standardised by the CIE in 1924 ⁵⁸ and forms the basis of current photometry ⁵⁹ .

Colorimetry. We implement the following colorimetric calculations:

•   CIE 1931 xy chromaticity (2° observer). The chromaticity coordinates are a way to identify the colour appearance of a spectrum. The CIE 1931 xy chromaticity diagram, also called the horseshoe, is based on the XYZ colour matching functions standardised by the CIE in 1931 ⁶⁰ based on 2° colour matching experiments by Wright ⁶¹ and Guild ⁶² . The chromaticity coordinates are calculated by weighting the spectrum by the x ¯ ( λ), y ¯ ( λ), and z ¯ ( λ) colour matching functions, yielding tristimulus coordinates X, Y and Z and then normalising: x = X X + Y + Z and y = X X + Y + Z . It is useful to note that CIE 1931 y ¯ ( λ) and CIE 1924 V( λ) are equivalent.

•   CIE 1964 x ₁₀y ₁₀ chromaticity (10° observer). The CIE has also standardised 10° colour matching functions x ¯ ₁₀( λ), y ¯ ₁₀( λ), and z ¯ ₁₀( λ), and associated chromaticity coordinates x ₁₀ and x ₁₀ ⁶³ . The 10° colour matching functions are based on psychophysical measurements done by Speranskaya ⁶⁴ and Stiles and Burch ⁶⁵ .

α-opic quantities following CIE S 026/E:2018. In 2018, the International Commission on Illumination (CIE, abbreviating the French Commission Internationale de l’Eclairage) released the new International Standard CIE S 026/E:2018 (“CIE System for Metrology of Optical Radiation for ipRGC-Influenced Responses to Light”, ⁵⁴ ), standardising the spectral sensitivities for ipRGC-mediated responses to light, and associated quantities. The spectral sensitivities of the L, M and S cones correspond to those developed by Stockman and colleagues ^{66, 67} and endorsed by the CIE ⁶⁸ . The rods’ spectral sensitivity corresponds to the standardised scotopic luminosity function, V ′ ( λ) ⁵⁹ , based on psychophysical measurements ⁶⁹ . The melanopsin spectral sensitivity curve in CIE S 026/E:2018 is the same as the one used in the influential Lucas et al. article ⁷⁰ and associated Irradiance Toolbox (see supplement of 70), based on previous proposals ^{71, 72} . To make calculations of CIE S 026/E:2018 related quantities accessible, the CIE released an Excel-spreadsheet based toolbox ⁵⁵ and associated user guide ⁷³ .

luox implements the following quantities based on CIE S 026/E:2018:

•   α-opic irradiance [mW/m ²] or radiance [mW/m ²/sr]. The α-opic irradiance or radiance of a spectrum is the weighted sum of the spectrum and the α-opic spectral sensitivity. Here and in the definitions for EDI/EDL and ELR below, “α-opic” is a placeholder term that can be filled by any of the five photoreceptors, the L, M and S cones, the rods and melanopsin. For example, the spectral irradiance or radiance weighted by the L cone spectral sensitivity is called the L-cone-opic irradiance or radiance, and the spectral irradiance or radiance weighted by the melanopsin spectral sensitivity is called the L-cone-opic irradiance or radiance.

•   α-opic equivalent daylight illuminance (EDI) and luminance (EDL). The α-opic equivalent daylight illuminance (EDI) or luminance (EDL) calculates the photopic (il)luminance of a standard daylight spectrum (CIE Standard Illuminant D65, corresponding approximately to daylight with a correlated colour temperature of 6500K) that matches the α-opic (ir)radiance. Alternatively stated, the EDI/EDL tells us the (il)luminance that a daylight would have to have to yield the same α-opic (ir)radiance.

•   α-opic efficacy of luminous radiation (ELR). The α-opic efficacy of luminous radiation is the ratio between the α-opic (ir)radiance and photopic (il)luminance, providing a simple, normalised indicator of the α-opic “content” of a spectrum. The melanopic ELR, i.e. the melanopic efficacy of luminous radiation, is similar to the the M/P ratio method proposed elsewhere ⁷⁴ .

In addition to linear notation, it is possible to toggle the display to exponential notation. While display of the calculated values is truncated to four decimal digits, the downloaded report, and indeed all underlying calculations, includes the numbers up to floating point precision (double-precision 64-bit binary format IEEE 754).

Spectral power distributions are typically stored as files in an MS Excel spreadsheet, comma-separated (CSV), XML (e.g. 75), JSON or other schema-based formats (e.g. 76). Storage of files requires an infrastructure, e.g., a server. To lose this requirement and enable the sharing of spectral power distribution data without sharing files, we (M.H.) developed a library with no external dependencies called spdurl written in JavaScript. spdurl encodes a spectral power distribution in a URL accurately and concisely. While the RFC for URLs (RFC 2616 ⁷⁷ ) does not specify an upper length limit, many web browsers may truncate it to 2 kB, which we pragmatically adopt as the limit for URLs here.

spdurl exploits the following aspects of spectral distributions:

•   Wavelength sampling: Wavelengths are assumed to be uniformly spaced, allowing us to write only the first value and an increment, with the total number of samples implicit in the number of samples given. Some spectroradiometers produce nonuniform wavelength spacing, so we expect these users to resample to a uniform spacing, as with the rest of luox.

•   Compression: We compress the spectra using a scheme that encodes spectral bands in two URL-safe bytes each, across a variety of units. The measurement process within CCD spectrometers uses a shared shutter for all elements in the array, allowing us to share an exponent for all values. This is also often done in HDR formats, like Radiance RGBE ⁷⁸ . As a base for our shared exponent, we chose 2 , sacrificing 1/8 bit to quantisation, rather than 1/2 bit if we had used 2 as a base. We do not constrain the exponent value (large exponents just use more bytes), so extremely small and large values can be represented, but most exponents use one or two bytes. In this way, energy can be stored as a linear value even at very small irradiances without worrying about range limits. While the best available CCD spectrometer arrays are specified to measure 16 linear bits, real-life signal to noise is much lower. We began with an 18-bit mantissa, but subsequently determined that for most uses, 12 bits of gamma-encoded data were sufficient for our calculations. To balance the accuracy of smaller and larger values, we informally determined that γ = 2.0 gave lower error than linear or cubic encodings. We perform rounding to 12 bits to avoid quantisation bias, which may result in small changes in the spectrum and derived quantities.

•   String encoding: We encode the resulting string as a URL-safe base64 (RFC 4648 ⁷⁹ ), meaning that each 12-bit value can be written using two bytes, with no padding.

•   Spectral resolution limits: Since we use two bytes per value, this means that visible spectra can be encoded in a valid URL (2kB) down to about 0.5 nm spacing. Meters that have high spectral resolution may wish to resample to fewer values before encoding.

•   Spectral units: We use a dictionary of datatypes (30 to date), which can represent spectral quantities (so that “/nm” is common to all) using just 2-3 bytes. For instance, the shorthand “uwi” is used to represent “uW/cm ²/nm”. Additionally, action spectra, transmittance, radiance, and quantal units are available using similar short abbreviation given in the software. Many file formats assume the reader knows the units in use; in spdurl, we make no such assumption, and so, this field is required.

•   Meta-data specification: Measurement conditions, like time zone, date, location, and user-specified name are allowed as optional metadata, when there is space at the end.

As an example, our library can encode a spectral radiance distribution specified between 380 and 780 nm with 1 nm spacing using 804 bytes, and a 10 nm sample (36 bands) from an X-Rite meter can occupy only 90 bytes, as succinct as the following:

spdurl-encoded spectral power distributions can be shared across platforms, e.g., in luox:

and in fluxometer:

spdurl (RRID: SCR_020992) is written in JavaScript for use on the web and node.js servers. It is available under the MIT License (code base at Github, npm package here). spdurl can be used as a standalone package independent of luox, and we hope that it will be attractive to other users.

To facilitate the sharing of URLs encoded in luox, we offer the deposition of encoded URLs in the Oxford Research Archive. Users need to complete a form with minimal information, and upon manual approval, a DOI will be assigned.

luox allows for graphical comparisons of uploaded spectra with a series of CIE reference spectra. These include Standard illuminant A , Standard illuminant D65, and Illuminants C, D50, D75, F1 through F12, FL3.1 through 3.15, HP1 through HP5, LED-B1 through LED-B5, and LED-BH1, LED-RGB1, LED-V1, LED-V2 ⁸⁰ .