Post on 05-Aug-2020
transcript
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)