The Inverse Square Law: the mathematics of light in product photographyThe Inverse Square Law: the mathematics of light in product photography

In 1604, in Prague, Johannes Kepler wrote in Astronomiae Pars Optica how light weakens as it travels away from its source: intensity is inversely proportional to the square of the distance. Put the light twice as far away and it drops to a quarter; three times as far, to a ninth. In more than four hundred years no photographer has negotiated this law away; every subtlety of product photography is a trick built around this single equation. A good product shot is not a good eye but the deliberate use of those tricks.

The first consequence of the inverse square law in the studio looks unexpected: the easiest way to darken a background is not to turn the light off but to bring it closer to the product. If the light is thirty centimeters from the product and the background stands a meter and a half farther back, the background receives one twenty-fifth of the light the product does; expose for the product and the background falls to black on its own. Pull the same light back to three meters and the difference between product and background shrinks; the background turns gray. The secret of black-background "hero" product photographs is not black cloth but distance.

Photographers count this falloff in "stops": each stop is a halving of the light. Doubling the distance is a loss of two stops. The unit is no accident; as Weber and Fechner measured in the nineteenth century, the eye perceives light logarithmically, so twice the light looks not "twice as bright" but "one step brighter." The entire exposure scale is drawn to this curve of human perception.

The sentence "a big light makes soft shadows" is incomplete. The sun is the largest light source we know, and at noon it casts the hardest shadow; the reason is that from 150 million kilometers away it covers only a half-degree disk in the sky. What determines softness is the angular size of the source relative to the product: a one-meter softbox fifty centimeters from the product is an enormous source; five meters away it is a small point, and its shadows harden. The penumbra of a shadow grows with the angle the source subtends at the product.

Light: Science and Magic by Fil Hunter, Steven Biver, and Paul Fuqua, first published in 1990, made these principles the standard text of photographic education and added a concept: the "family of angles." Every surface reflects light into the lens only from a particular range of angles; if the light falls inside that family the reflection shows, and if it falls outside, it does not. The way to remove an unwanted reflection from glossy packaging is not to dim the light but to move it out of that family.

The white line on a glass bottle is not "glare" but the mirror image of the light source. This is why long, narrow vertical softboxes are used in bottle photography: the thin white line along the edge of the bottle is that softbox itself. Change the shape of the source and you change the shape of the highlight on the product; a round source leaves a round highlight, a rectangular source a rectangular one. The product photographer designs not the light but the light's reflection on the product.

Sometimes no reflection is wanted at all. In 1929, Edwin Land developed an inexpensive sheet polarizing filter; when two polarizing filters are crossed, one on the light and one on the lens, the surface reflection disappears and the color underneath stays as it is. This method, called cross-polarization, is the only reliable way to photograph glossy printed boxes, glazed ceramics, and leather with color accuracy.

The color of light is measured as a temperature because that is how physics works: a heated body gives off red light first, then white, then blue. A tungsten lamp is roughly 3,200 Kelvin, the noon sun 5,500. But two lights can have the same Kelvin value and still render colors differently; LEDs are the most frequent example. The color rendering index (CRI) was defined in the 1960s to measure this difference; in 2015 the Illuminating Engineering Society replaced it with the TM-30 metric because the index missed failures in saturated colors. A high-CRI LED can still shift a red package toward brown.

This is why calibration is done with a chart, not with the light. In 1976, McCamy, Marcus, and Davidson published a twenty-four-color chart in the Journal of Applied Photographic Engineering: the ColorChecker. In every setup one frame is shot with the chart, and software corrects the whole series against the chart's known values. Whether a color is "right" is stated in ΔE; a difference below a value of two cannot be told apart unless the two are set side by side. A catalog shot without a chart is a catalog that does not know what light it was shot under, and the buyer learns the product's color wrong.

Stopping down the aperture to get the whole product sharp has a limit: past f/16 diffraction sets in and the image softens; optical scientists call this the Airy disk. There are two ways around it. The first is the principle patented in 1904 by the Austrian officer Theodor Scheimpflug: when the lens plane is tilted, the plane of focus tilts with it, so a product lying flat on a table is sharp from front to back; tilt-shift lenses work on this principle. The second is focus stacking: the same frame is shot at different focus points, and software merges the sharp region of each frame. In jewelry and small-part photography, single-frame sharpness is physically impossible; sharpness is computed.

In 2014, Wei Di and colleagues at eBay's research lab measured the effect of photo quality on sales across millions of listings and published the results at the WSDM conference: well-lit images with clean backgrounds that showed the product large significantly raised the likelihood that the same product at the same price would sell. The "quality" of a photograph here was not art but a handful of measurable properties: contrast, simplicity of the background, the share of the frame the product filled.

Marketplaces turned this finding into a rule. For the main product image Amazon requires a pure white background (RGB 255,255,255), a product that fills at least 85 percent of the frame, and a side of at least 1,000 pixels for zoom; an image that breaks the rule is not published. The technical standard is not a creative limit but a ticket of entry; the catalog's beautifully composed frame is rejected on the marketplace, and the marketplace's white frame looks lifeless in the catalog. The two channels ask for two separate frames, and both are taken on the same shooting day with the same lighting setup.

The consistency of a product series depends on every product being shot under the same light, and that applies to the new product added a year later as well. This is why every setup is written down: the type and size of the source, its distance and angle to the product, its height, its power, the camera height, the focal length, the chart frame. Hunter's family of angles, Kepler's distance, and McCamy's chart fit on a single page; without that page "the same light" is a memory, with it a measurement.

Our protocol is summed up in three frames: a white technical frame for the marketplace, a composed frame for the catalog, and an in-use frame for social media; all three are variations of the same setup. A ColorChecker is shot in every setup, and the series is corrected to a ΔE 2 threshold. On glossy surfaces cross-polarization is standard. Black-background hero frames are built with distance, white-background frames with a separate background light. The setup card is archived with the files; the raw files, the chart, and the script are the starting point for next year's shoot.

Kepler's equation has not changed in four hundred years. Product photography is the art of using that equation in the product's favor.

Kepler, J. (1604). Ad Vitellionem Paralipomena, quibus Astronomiae Pars Optica traditur. Frankfurt.

Fechner, G. T. (1860). Elemente der Psychophysik. Leipzig (Weber–Fechner law).

Hunter, F., Biver, S. & Fuqua, P. (1990; 5th ed. 2015). Light: Science and Magic: An Introduction to Photographic Lighting. Focal Press.

Land, E. H. (1929/1933). Polarizing refracting bodies. US Patent 1,918,848.

McCamy, C. S., Marcus, H. & Davidson, J. G. (1976). A color-rendition chart. Journal of Applied Photographic Engineering, 2(3), 95–99.

Illuminating Engineering Society (2015). IES TM-30-15: Method for Evaluating Light Source Color Rendition.

Scheimpflug, T. (1904). Improved method and apparatus for the systematic alteration or distortion of plane pictures. British Patent 1196/1904.

Di, W., Sundaresan, N., Piramuthu, R. & Bhardwaj, A. (2014). Is a picture really worth a thousand words? On the role of images in e-commerce. WSDM '14, 633–642.

Amazon Seller Central, product image requirements (pure white background, 85 percent fill, 1,000-pixel zoom threshold).