---
title: "How a white sphere compares a lamp’s total output"
description: "An integrating sphere mixes light through diffuse reflections. Reference comparisons must include port loss and absorption by the sample or source."
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last_modified: "2026-11-03"
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Inside the instrument

# How a white sphere compares a lamp’s total output

An integrating sphere sends light from different directions through repeated reflections at a white inner wall. A small detector can then compare total source output. Replacing a lamp with a known reference connects the detector-signal ratio to a relative radiant flux.

Sandbox Physics · 2026-11-03

## A forward-facing detector misses the sideways light

A small lamp can emit forward, sideways and backward. A photodetector placed in front receives only part of that output. Turn the lamp and its reading may change even when the lamp’s total emitted power stays constant. A total-output comparison needs to collect light from more directions.

Inside a hollow white sphere, light has repeated opportunities to approach the detector. A diffuse wall spreads arriving light across directions, unlike a mirror that favors one reflected direction. After repeated encounters, the reading depends less on the initial direction of emission. This mixing is the purpose of the integrating sphere.

Sources: [1]

## The same light can visit the wall several times

White walls still absorb light. Suppose each reflection retains ninety-five percent and temporarily ignore openings. After twenty reflections, about thirty-six percent remains. A higher reflectance allows more light to survive many encounters and illuminate the enclosure more thoroughly.

Counting every arrival at a wall counts the same packet repeatedly. The packet finally ends at an absorbing surface, the detector or an escape port. A high sum of wall visits therefore describes a longer journey for the incoming light.

A port interrupts this circulation. Light can leave whenever it reaches an opening, so a modest hole can produce a substantial loss after repeated reflections. An instrument must include every entrance, detector and auxiliary opening, and distinguish an open black port from one filled with a reflecting sample.

Sources: [1]

## A detector baffle becomes another optical surface

A detector that directly sees the source or its bright first-illumination spot can respond too strongly to that particular path. A baffle blocks the view so the detector receives mainly mixed light.

The baffle also reflects and absorbs. Rays can reach its front, back and edge. Treating the enclosure as a uniform empty sphere would omit these interactions. Ideal sphere formulas explain useful trends; the actual apparatus needs its own geometry and calibration.

Sources: [1]

## A dark replacement sample makes the sphere darker too

To measure reflectance, place a known white reference at a sample port, illuminate it, and then substitute the unknown surface. The sphere collects light reflected into many directions of the inward hemisphere. Comparing detector signals gives information about the sample’s reflected fraction.

A darker sample reflects less on the first encounter. It also absorbs more of the light that later returns to its port. Substitution therefore changes both the initial reflection and the survival of circulating light. A simple detector ratio combines these effects. The resulting change in sphere response is called substitution error.

A correction needs the sample-port size, surface reflectances and the return illumination of the sample. Another known surface, withheld from calibration, tests a new predicted signal. A defined incident direction, collection range and wavelength make clear which reflectance the measurement describes.

Sources: [2] [3]

## Changing the lamp can change the enclosure response

A known lamp can similarly serve as a reference for total output. Lamp glass, bases and supports absorb returning light. Different shapes or positions can change the sphere throughput. Precision measurements use additional illumination to compare absorption with each unlit lamp installed and correct the substitution.

Color matters too: wall reflectance and detector sensitivity vary with wavelength. Matching spectra or calibrating wavelength by wavelength connects a signal ratio to the intended source output. The white enclosure brings many directions together; the known reference gives the resulting detector signal a physical comparison.

Sources: [1] [4]

## [Follow the surfaces visited by circulating light](https://sandboxphysics.com/labs/integrating-sphere-radiometer/)

Compare sample substitution and source flux, alter ports and the baffle, and inspect corrections from retained counts.

The monochromatic Lambertian model includes sample reillumination, baffle, ports and source-housing absorption, with conditional relative measurements.

## Sources and further reading

1. [Labsphere — Integrating Sphere Radiometry and Photometry (2017)](https://www.labsphere.com/wp-content/uploads/2021/09/Integrating-Sphere-Radiometry-and-Photometry.pdf)

   Printed pages3–5 derive the diffuse exchange and multiplier; pages10–12 discuss baffles and calibration; pages18–21 cover source substitution and absorption.

2. [Labsphere — Integrating Sphere Theory and Applications (2017)](https://labsphere.com/wp-content/uploads/2021/09/Integrating-Sphere-Theory-and-Applications.pdf)

   Reflectance/transmittance and substitution-sphere sections explain how a replaced sample changes average reflectance and throughput.

3. [NIST — Reference Integrating Sphere for Spectral Reflectance](https://www.nist.gov/laboratories/tools-instruments/reference-integrating-sphere-spectral-reflectance)

   A real directional-hemispherical reflectance instrument uses tunable quasi-monochromatic illumination and defined samples.

4. [Shimadzu — How to Choose Integrating Spheres and White Reference Plates](https://www.shimadzu.com/an/service-support/technical-support/technical-information/uv-vis/uv-ap/white/index.html)

   Wall coating and reference reflectance vary with wavelength and influence the measured comparison.

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