In the introduction for this blog series, I gave an overarching breakdown of some of the fundamental concepts of light and how we interact with it on a daily basis. It can be described, interpreted, and manipulated in a variety of ways in order to better understand how it is impacting a space and how we, as humans, interact with it to shape our fundamental understanding of the world around us. In this installment of the series, I am going to provide a brief breakdown of how we can mathematically quantify light in order to foster a greater understanding of how specific light sources and their associated luminous flux are illuminating the world around us. However, I am not going to walk you through the exact methodology and calculation process that I learned in school, that took two full semesters in my degree to walk through and actually apply (in addition to the two years of prerequisite calculus, physics, and computer science courses). It’s an intricate flux balance wherein space geometry, source characteristics and emittance, and surface characteristics are all input variables that determine how light travels through, reflects, and refracts in a space until it reaches an equilibrium. This article will serve to be the down and dirty basics, giving you the fundamentals so you can understand what different measurements mean and how those measurements are used to design, optimize, and curate healthy environments.

Let’s start at the very beginning by defining light. Light is electromagnetic energy, a part of the electromagnetic spectrum that is the entire distribution of electromagnetic radiation according to frequency or wavelength. The spectrum ranges from radio waves to gamma waves, with the visible spectrum existing somewhere in the middle and being characterized as the only part of the electromagnetic spectrum that is visible to the human eye. Light is a type of radiation that moves through space and normally travels in straight lines and interacts with objects in space by reflecting and refracting. More specifically, “electromagnetic spectrum radiation” is a stream of photons, massless particles that travel with wavelike properties that are characterized as being the smallest quantity of energy that can be transported that carries energy proportional to the radiation frequency but has zero rest mass. Each color associated with the visible spectrum has a corresponding wavelength, between around 380nm and 700nm. Shorter wavelengths are associated with “cooler” colors, such as violet at around 380nm; longer wavelengths are associated with “warmer” colors, such as red at around 700nm. The color information is not as important when we are simply performing a lighting calculation, but will become more important later on as we start to examine how humans interpret different lighting scenarios.

Now that we have a basic working definition of light, we can start to dissect how light is emitted from artificial sources (aka the light fixtures that are probably above you right now). For the sake of clarity and so my professors don’t roll over in their graves, I am going to be referring to light fixtures/lights as luminaires, complete lighting units that contain lamps, optics, and associated wiring. The distribution associated with a specific luminaire is primarily based on the optics within the luminaire and the housing itself, it is basically just a fancy way of referencing the spatial distribution of light as it exits the fixture. If you have ever looked at a lighting specification sheet, there is a section that graphically shows and describes the distribution associated with that specific luminaire and/or specification. There are countless types of distributions, but I want to focus on the general concept of direct/indirect lighting and the two most common types of distribution patterns - cosine and batwing. “Direct” lighting distributions refer to when the light being emitted from the luminaire is all projected downwards into the space; whereas, “indirect” lighting distributions refer to luminaires where the lighting is projected upwards into the space. There are also combinations/derivations of both, you will see direct-indirect (majority of the light is directed downwards with a smaller proportion being directed upwards) and indirect-direct (majority of the light is directed upwards with a smaller proportion being directed downwards). These are just different methods of directing light into the space to achieve different lighting effects and levels. In regards to specific shapes of lighting distributions, the two that I want to note are the standard cosine distribution and the batwing distribution. A cosine distribution will graphically look more like an oval with the majority of the light being directed straight down from the source; a batwing distribution will graphically look more like what the name implies, a batwing with the majority of the light being more angled outward from the source. The distribution is important to note because it determines how the light and the corresponding intensity is being spatially distributed and will impact calculations based on how the light then interacts with the rest of the environment.

At this point, we have a general understanding of what light is and how it is emitted from a source into a space and the fun can begin. Like any good calculation, you have to start by defining and understanding the standard units of measurement that you will be using. If I were being completely thorough I would step through the difference between radiance and irradiance as we dissect the difference between illuminance and luminous flux, but for the sake of not writing a ten page blog article we will keep it basic with illuminance calculations. Illuminance is defined as the amount of luminous flux per unit area and is the most common way that you will see lighting quantified. Depending on your standard unit system, you will see it defined as either lux (metric) or footcandles (fc - english). Lux represents the number of lumens per square meter and footcandles represents the number of lumens per square foot. Now you may be asking yourself, what’s a lumen? A lumen is a unit of luminous flux that is equal to the amount of light emitted per second in a unit solid angle of one steradian from a uniform source of one candela. What’s a candela? A candela is the base unit of luminous intensity, it is the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540 x 10^12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. Are these exact definitions super important for a general understanding of how we mathematically quantify light? No. Your biggest takeaways should be:

• Illuminance is the most common way of quantifying light and is a measure of the intensity of light that hits or passes through a surface → measured in lux and footcandles

• The lumen and the candela are base units for quantifying light → lumens describe the “amount” of light from a source output and candela describes the number of lumens within a beam angle/direction

When I was working for an MEP firm, I ran a lot of lighting calculations that would output illuminance values to ensure that designs were meeting code requirements and design guidelines. In practice, we just used the lighting software that was already developed to input space geometry, reflectances, objects, etc and locate and aim the specified luminaires to run the calculations. In school, we had to first do all of these calculations by hand and then develop and code the software ourselves. Again, I am not walking you through those calculations. However, I do want to touch on the basic equation for calculating illuminance, the inverse square cosine law. Simply put, this law states that the illuminance at a point is inversely proportional to the square of the distance of the point from the point source of light. If you haven’t watched the reel that I posted on my Instagram, I would highly recommend watching it because I walk you through a basic calculation that serves as a simplified “gut check” for a lighting scenario by measuring illuminance at a point from a point source that is located directly below the source. I say “gut check” because it gives you a good general idea of where your illuminance levels should be and the amount of light that would be in the space or on a specific task/work area.

 Let’s run a quick recap:

• Light is defined as a form of radiant energy on the electromagnetic spectrum and is characterized as the wavelengths that are visible to the human eye.

• A luminaire is a complete lighting unit that contains source lamps, optics, and associated wiring. The optics and housing design of the luminaire determine the distribution, or the spatial distribution of the light as it exits the luminaire.

• The standard units of light are the candela, lumen, and fc/lux (illuminance).

• Illuminance is the most common measurement used to describe the “amount” of light in a space or on a work plane and can be calculated as we determine luminous flux per unit area based on source characteristics and the characteristics of a space.

But why does this matter? What do we do with this information? That’s the cool part, there are actually pages and pages of recommendations for illuminance levels that have been developed from the Illuminating Engineering Society (IES) that provide guidelines for light levels based on associated tasks/room purposes. The recommendations take into account the visual acuity necessary for certain tasks and light levels required for humans to operate efficiently and effectively in a space. In fact, the level of specificity even takes into account occupant age and adjusts based on how our vision changes as we age. For each space, the guidelines are designated with minimum, standard, and maximum values that lighting engineers and designers use to appropriately light a space. Two types of spaces and their associated recommendations I want to highlight are:

• Offices/Classrooms: 20-50fc depending on application (usually 30fc is a good rule of thumb)

• Residential: 5-30fc (30 fc is usually in bathrooms or on cooking surfaces, while 5fc is in living spaces/bedrooms)

I am highlighting these spaces because we have all been in them and have experienced the associated levels of light, therefore, it gives you a good reference for what “30 fc” looks and feels like. Odds are the office you are sitting in is probably around that 20-30fc range, pay attention to what that feels like and looks like because it gives you a reference point and connects a numeric value to a qualitative state. You can use this information to light spaces appropriately for the tasks being performed and not “over-light” it, it creates more comfortable and effective spaces that enhance productivity and promote healthy living and working spaces.

With a basic understanding of how we measure and mathematically quantify light, we can start to look a bit deeper into how humans interact with the light and use it to shape and understand the world and space around us. In the next part of this series, I will break down how these numbers, photons, and wavelengths are actually interpreted and understood via the visual pathway in our brain.