Additive and Subtractive Trichromacy in Photographic Color Reproduction

Hello. The previous lesson followed the physical support of a photographic image, from metal plates to flexible film. Changing the support made photographs easier to make and carry, but it did not answer a different question: how can a photograph preserve color when its light-sensitive material records exposure rather than a complete spectrum at every point?

The answer joins visual physiology to optical engineering. In about 40 minutes, we will derive why three suitably chosen records can reproduce many perceived colors, then distinguish two ways of turning those records back into an image: adding colored light and selectively absorbing light with dyes. This prepares us to examine how color film actually makes and processes its separate records in the next lesson.

Why three records can be enough

Consider one small patch of a scene. Its light has a spectral distribution $L(\lambda )$: power at each wavelength $\lambda$. Human color vision does not report that entire function. Instead, the three classes of cone photoreceptor have different, overlapping spectral sensitivities. In a simplified linear model, their responses are

where $s_i(\lambda )$ includes the sensitivity of one cone class. The integral maps a function of wavelength to three numbers. It necessarily loses information: distinct spectra can produce the same three responses and therefore look alike under specified viewing conditions. Such spectra are metamers.

Read the “Additive mixing” section of Stanford’s Additive versus subtractive color mixing before applying this idea to a camera. The examples make the difference between matching a spectrum and matching its appearance concrete.

A camera can obtain three measurements by exposing through three different color filters. If the underlying recording material has sensitivity $h(\lambda )$ and filter $j$ has transmission $F_j(\lambda )$, an idealized channel exposure is

Here $R$, $G$, and $B$ label broadly red-, green-, and blue-selective records, not single wavelengths. A filter cannot make a material responsive to light it cannot detect; practical color separation also required sensitivity across the relevant spectral regions.

The cone responses and photographic records are both triples, but they are not automatically the same triple. If a matrix applied to the three camera measurements predicts the three cone responses well over the spectra of interest, the records contain much of what is needed for visual reproduction. Real filters, recording materials, dyes, illumination, and observers depart from that ideal. Conversely, once two scene spectra produce the same three camera measurements, no later processing can recover which spectrum was originally present.

This is the engineering bargain behind photographic trichromacy. A photograph generally need not reconstruct every wavelength reflected by a subject. It needs to produce appropriate visual responses when viewed—within the limits of its capture filters, reproduction method, and viewing conditions.

Additive reproduction: making the light

Suppose the three records have been turned into positive images, so that a bright red portion of the subject gives a strong red-channel output. Put each positive image in a projector with its corresponding red, green, or blue filter and register the three projections on a screen. At any point, the outgoing spectrum is the sum of the light contributed by the three projectors:

where $p_R,p_G,p_B$ are the projector spectra and the nonnegative coefficients $a_R,a_G,a_B$ vary across the image. The perceived color depends on the three resulting cone responses. If all three contributions are appropriately balanced, their mixture can look white; red and green contributions can look yellow even though the projectors need not emit yellow wavelengths.

The George Eastman Museum’s Color Photography shows this photographic scheme and a second additive arrangement, in which tiny colored regions lie side by side rather than three projections occupying the same point.

The two arrangements share a perceptual principle but impose different mechanical constraints. Three separate exposures demand registration; movement between them can produce colored edges or mismatched subjects. A screen plate puts color-selective regions into one photographic object, allowing a single exposure, but each region passes only part of the incoming light and occupies finite image area. That costs light efficiency and limits spatial detail. When the regions are too small to distinguish at normal viewing distance, your visual system combines their contributions.

Additive reproduction also has a gamut limit. For fixed projector spectra, the available colors come from nonnegative amounts of those spectra. Some desired cone-response triples cannot be made from that particular set without requiring a “negative” amount of one primary. Choosing three primaries is therefore an optical-design decision, not a claim that any three colored lights reproduce every visible color.

Subtractive reproduction: shaping light already present

A color transparency or color print operates differently. It starts with illumination and controls which wavelengths pass through or reflect from each image location. If light with spectrum $L_{\mathrm{in}}(\lambda )$ passes through stacked dye layers with transmissions $T_C,T_M,T_Y$, the outgoing spectrum is approximately

The multiplication describes successive filtering. “Subtractive” means that dyes remove portions of the incident spectrum; it does not mean that physical spectra are subtracted from one another by an arithmetic minus sign.

The dye names describe the colors they transmit or reflect when viewed under suitable white light:

• Cyan preferentially removes red and passes green and blue.
• Magenta preferentially removes green and passes red and blue.
• Yellow preferentially removes blue and passes red and green.

Thus cyan and yellow together can leave principally green light; magenta and yellow can leave red; cyan and magenta can leave blue. With no dye, a clear transparency passes its illuminant. Strong absorption by all three ideally leaves little light.

Stanford’s subtractive examples are worth reading because they expose a subtle failure of the usual “mix three colors” sketch: filters that look individually like suitable primaries do not necessarily have the spectral overlap needed to make useful mixtures.

An ideal three-band model makes the dye roles particularly clear. Let $q_R,q_G,q_B$ be the fractions of red-, green-, and blue-band illumination that should emerge from a picture element. Cyan controls $q_R$, magenta controls $q_G$, and yellow controls $q_B$. If dye density is defined in each relevant band as

then, in that idealization,

This is why a positive color transparency must have little cyan density where the subject should appear red, but substantial cyan density where red light should be suppressed. The logarithm is useful physically: because transmissions of stacked layers multiply, their optical densities add. Real dyes have broad, imperfect absorption spectra, so this diagonal three-band model is a starting point rather than an exact recipe for color matching.

The diagram below traces scene colors through three separate records to subtractive dye images in a positive transparency. Treat its blue, green, and red bands as an idealization: photographic layers and dyes respond over overlapping wavelength ranges.

Look at the tree as a consistency check on the diagram. Its green area should pass green while suppressing red and blue. Cyan dye suppresses red; yellow dye suppresses blue. Their overlap leaves principally green. The red roof instead requires magenta and yellow, which suppress green and blue while permitting red. These are statements about the finished positive image, not yet about which chemical reaction deposits each dye.

Where capture and reproduction meet

It helps to keep three distinct operations in view:

1. Color separation at capture: three spectrally different measurements retain information that one undifferentiated exposure would lose.
2. Formation of image values: those measurements must be converted into appropriately positioned positive outputs—or into an intermediate negative that will be inverted during printing.
3. Color combination in viewing: light contributions add in a projection or fine screen; dye transmissions multiply in a transparency or print.

The second operation prevents a common sign error. A camera record strongly exposed by red light does not imply that a positive transparency should contain much cyan dye at that position. Cyan blocks red, so the finished positive needs low cyan density there. A color negative can encode the opposite density relationship because a later printing step reverses it. The capture principle—three color-selective records—remains related, while the required density relationship depends on whether the final object is a negative or a positive.

Nor is matching under one illuminant a guarantee of matching under another. The transmitted spectrum depends on the illuminant in the equation above. Two dye combinations may look alike under one light source yet differ under another, just as two scene spectra can be metamers. This makes color reproduction a coupled problem of spectral sensitivities, dye absorption, illumination, and human vision rather than a simple assignment of three color names.

Conclusion

Trichromacy makes photographic color possible because visual matching generally requires control of three response channels, not a wavelength-by-wavelength copy of the scene. Additive methods combine controlled red-, green-, and blue-weighted light; subtractive methods control that light by stacking cyan, magenta, and yellow absorbers. Their respective spectra add and multiply, and neither method escapes limits imposed by real filters, dyes, registration, illumination, and gamut.

We have established what three color records and three dye controls must accomplish. Next, we will examine how multilayer films place those records in one material and chemically turn exposures into either negative or reversal color images.