Towards Understanding Photogrammetric Refraction

in Large Volume MetrologyStuart Robson, Stephen Kyle, Lindsay MacDonald and Mark Shortis

Luminar is an EU funded project seeking to enhance our understanding of the influence of environmental variations on

optical metrology. The UCL component is looking at better understanding and subsequent mitigation of environmental

refraction using photogrammetric techniques.

Contact: s.robson@ucl.ac.uk

Gower Street, London, WC1E 6BT

Objective: An analytical estimation of the pointing and displacement

errors due to refraction caused primarily by temperature gradients in the

local working environment.

Basic Concept: In the current, first evaluation, the atmosphere in a

measurement area is defined a simple model of horizontal layers of dry

air, each at a particular temperature.

Rays are traced through the air, applying Snell’s Law at each layer

interface in order to calculate a change of direction of the ray as it passes

from one layer to the other.

Snell’s Law relates the angle of

incidence (i) of a ray to the angle of

refraction (r) where n’ is the refractive

index on the side of the incoming ray

and n the refractive index on the side

of the outgoing ray.

Formula for refractive index: Several simplified formulae for the refractive

index of air could be used in the simulation. One of the options currently

used is by Williams & Kahmen, Geodetic Refraction, 1984. Note that this

formula gives the refractivity which is (1 – refractive index).

How the rays bend:

Example scenario: An observing position and target are separated by

some 6m horizontally and 4m vertically. Given a 12oC temperature

gradation from cold on the floor to hot near the ceiling, the apparent

target position is displaced approx. 45mm from the actual position.

First Experiments: Observing a series of optical rail mounted target plates

imaged with a 200mm Nikon f/4 lens into a C-mount IDS uEye camera.

Targets are imaged at 2 Hz with real time target image measurement in

ambient and turbulent conditions (fan blower across the lines of sight). The

following graphics show plots of standard deviation for each of 9 target

images over a 100 frame sequence highlighting the capability of this sensor

to detect change from a steady state.

Ambient

Fan blowing

Summary:

• Initial experiments demonstrate a clear variation in the stability of digital

photogrammetric retro reflective target images that is attributable to

variation of the air flow along a measurement sight line.

•The system used to make these measurements is now part of a series of

laboratory tests being carried by UCL at NPL. These tests will attempt to

link the mathematical model for geodetic refraction to that reproducible in

a highly stable metrology laboratory. Subsequent experiments will

expand the work to an industrial environment.

• It is envisaged that a combination of direct observation and advanced

simulation will provide a new photogrammetric capability for complex

environments.

Atmospheric simulation model where coloured bands represent variations in temperature

Ray bending within an atmospheric simulation model with vertically increasing temperature

Ray bending within an atmospheric simulation model with vertically decreasing temperature

Example ray bending scenario with a 12oC temperature variation giving rise to a 45mm target shift

Targets, targets images, camera system and sequential target image standard deviations for 9

targets over a 100 frame sequence with and without turbulent air

n’ – sin(i) = n – sin(r)