GB2275770A

GB2275770A - X-Y position based on reflected light

Info

Publication number: GB2275770A
Application number: GB9304366A
Authority: GB
Inventors: Augustine Kamugisha Tibazarwa
Original assignee: Individual
Current assignee: Individual
Priority date: 1993-03-04
Filing date: 1993-03-04
Publication date: 1994-09-07
Also published as: GB9304366D0

Abstract

A bounded region 1 has a light source and a light reflective and sensitive boundary. The rays of the source may be made to take a definite (deterministic) path, and thus produce a deterministic light intensity profile on the light sensitive boundary. Thus an opaque object placed in the rays' path, will alter the expected intensity. By comparing the expected and the measured intensity profiles of the sensor, the straight line containing the opaque object can then be established. A second light source producing a second beam will give a different straight line, and the spatial intersection of these two lines is thus the X-Y position of the object. By appropriately switching on/off the two sources, it should be possible to minimize interference. <IMAGE>

Description

X-Y POSITION BASED ON REFLECTED LIC,,, This invention relates to mathematical expressions for reflected light rays, that can be converted into a computer algorithm.

X-Y position determining systems are well known and based on a variety of principles.

No particular principle has become completely dominant, and existing systems are being continuously improved for reliability and wider applications.

According to the present invention, a ray of light, confined in a two dimensional rectilinear region, can be treated as two independent but spatially correlated, rays of light ( Ray X and Ray Y), travelling perpendicular to each other. Choosing directions of the two rays to coincide with the directions of the region's boundaries can yield a fast algorithm for determining the original ray's ( Ray M) path (described by locations on the region's Boundary 1, where the ray is reflected).

By appropriately choosing two light sources, a simple algorithm can be derived to determine the (x,y) coordinates of an opaque object in the region, Region 1.

A specific illustration of the invention will now be described by way of example with reference to the accompanying drawings in which : Figure 1 shows the rectilinear region, Region 1, bounded by Boundary 1, with the main Ray M originating from a light source at (Xo,Yo) with a beam angular spread 2e Figure 2 shows the light intensity profile in one comer of Region 1.

Figure 3 shows another possible incident beam scenario.

Figure 4 shows another possible incident beam scenario.

Figure 5 shows another possible incident beam scenario.

Each of the above figures shows the relevance and applicability of the various mathematical expressions.

A ray M originating at (Xo,Yo) in a direction 0 (in a cartesian coordinates system) at speed c can be considered as 2 component rays, one in the x direction at speed C close and the other in the y direction at speed C sinO The time Tx(Nx) that Ray X hits, for the Nth occasion, Boundary 1 at x=O and x=Xb alternately can be calculated and stored sequentially.

Similarly, Ty(Ny) can be compiled for the ray in the yclirection. The general formula is

whereby, for j=x, f(O-)=cose, and for j=y, f(43)=sinl3 The 2 tables can then be used as look-up tables, to determine whereabouts on Boundary 1 the ray will hit.

So, if the next reflection is at time T=Tx, then boundary 1 will be hit at y=T.csin&commat;+Y0 If instead the reflection is at T=Ty, then Boundary 1 will be hit at X = T.C COSo + X0 The boundary consists of light reflecting material, as well as light intensity detectors.

Thus, by making use of the Tj(Nj) with (j: x, y), the "theoretical" ray path can be established, and together with the detectors profile, ie intensity of light recorded by detectors, it is possible to determine the straight line containing an opaque object in the region.

By using 2 suitably arranged sources of light, the exact position of the object can then be determined.

In practice, a light source will produce a beam of light. In figures 1-7 we model the beam as having a Gaussian standard deviation, of Our ray diagram can therefore be modelled as in Fig 1, ie a central ray M, flanked by Ray 1 and Ray 2.

The detectors' light intensity profile then changes slightly, such that for a given beam incidence on the boundary, a contiguous number of detectors may record light.

Figure 1 shows one particular incident beam scenario. The light intensity on the boundary y=Yb will maintain the Gaussian distribution, but in such a way as to reflect the inequalities in the differences between Ray M, and Ray 1 & Ray 2 along the edge.

Given only the location of the light source (Xo,Yo), the original beam direction (3, and 112 the beam spread, , it should be possible to approximate the theoretical light intensity profile for the detectors.

A measured deviation from this, for a particular detector, would imply an opaque object blocking the beam. This object lies in the straight line joining this detector, and the last set of detectors whereby the measured intensity profile agreed with the theoretical profile.

From Figure 1,

where

A=(Y/b#Y2+L)/Yb-Ym+L) with

From Fig 1, it can be seen that using trigonometry, it is possible to determine the locations of the edges of the beam (ie, Ray 1 and Ray 2) on Boundary 1 and establish the theoretical light profile along the boundary.

Figure 3 shows a comer situation, and shows the need for Rc. This can be thought of as the distance covered by the central part of the beam, from the light source. It is assumed that the angular beam spread 2 , is maintained.

X= X'tanP and assuming a Gaussian distribution of light intensity is maintained, sinP =Rcsine/(X +Z) Using these formulae, it is possible to determine the light profile along the corner Rc is only needed in the rare corner situation. The formula takes some 25 computations, and is seldom applied, maybe once in 20 reflections. An easier ( 7 computations) calculation for Rc is to continuously update the distance travelled by the middle ray. This iterative method means in every 20 reflections when the value is actually used (on average), some 140 computations would have been done.

Figure 4 shows how the formula for Rc changes when the edge of beam, depicted by Ray 1, and the centre of beam, ray M, were not reflected off the same edge.

Here,

with Z7=L These formulae also apply to Figure 4.

Figure 5 shows a situation where the ray M and ray 2 come from the same boundary edge, but do not hit the opposite edge.

Further corrections to the theoretical profile can be made, by considering other sources of errors. In general errors due to mirror (ie, reflective sections of Boundary 1) misalignment angle , will on average, cause an angular correction Q(n) , such that

where n is the nth reflection.

If #1=#2, and p(#1)=p(#2) and p(#) is symmetric (eg Gaussian), then

Claims

Claims 1 A ray of light, confined in a 2 dimensional rectilinear region, can be treated as 2 independent but spatially correlated, rays of light, travelling perpendicular to each other.
2 A beam of light, consisting of rays that can be considered as in Claim 1. to approximate the path of the beam.
3 A beam of light or beams of light, as in Claim 2, that can be modelled based on considerations outlined herein, and making use of consequent formulae to approximate the intensity profile on boundary.