ed by the 
^ with an 
nology for 
rior surface 
parent that a 
discussions 
density and 
nterpretable 
ind corneal 
about the 
[he cameras 
fitted with 
itioned at 
umeras were 
type so that 
his required 
the limited 
close to be 
operational 
iccess to the 
lerate close 
rcome these 
beamsplitter 
appeared to 
ar technique 
X measuring 
The control 
ugh a thin 
n accurately 
inated from 
The control 
he cameras, 
1 onto the 
ope. This 
ight of the 
] relative to 
: 
  
  
  
  
A variety of methods of marking the cornea were considered 
including talc, as per Bonnet's work (Bonnet 1959, Le Grand 
1961, Bonnet and Cochet 1962) and alternatives to talc, 
particularly in combination with tear film stabilisers, as well 
as the self-luminance approaches of El Hage (1972c), 
Warnicki et al (1988) and Banda and Muller (1990). The 
method adopted uses marked ultra-thin (10pm) hydrogel soft 
contact lenses. This approach proved satisfactory for the 
prototype although a teflon material used by Thall (1993, 
1993 per com) would appear to have greater promise. The 
indications are that it is simpler to use, it is likely to be 
simpler to mark, or that a pattern of marks could be projected 
onto it. The instrument uses two optic fibre bundles to 
redirect a Mecablitz 45CT flash to the edge of the cornea 
where much of the light is internally reflected behind the 
cornea to back illuminate the contact lens. A third optic fibre 
bundle from the same flash is directed to the back of the 
control sphere. 
  
Figure 2. The control points imaged off the beamsplitter 
in the absence of an illuminated cornea. 
The calibration and verification of the system was completed 
using both the DLT and UNBASCI software (Abdel-Aziz 
and Karara 1971, Karara and Abdel-Aziz 1974, Marzan and 
Karara 1975, El-Hakim et al 1979). The DLT was used for 
routine data reduction. The photocoordinates of the object 
space control and the corneal reference marks were measured 
monoscopically using a Zeiss comparator and correlated 
prior to performing the camera calibration. 
It was instructive to make some estimates of the expected 
accuracy of the system and particularly to examine the likely 
effects of varying parameters such as convergence angle, 
base distance and object distance on the expected precision 
of object space coordinates. The geometry of the system was 
constrained by minimum object distances, by minimum depth 
of field considerations, and by the obstructions caused by the 
patient's brow and nose. The practical working range was 
found to be an object distance of between 27cm and 39cm, 
and convergence of between 15° and 30°. 
Formulae presented by Abdel-Aziz (1974) and Karara and 
Abdel-Aziz (1974) were used to investigated the expected 
precision of the solution for a range of practical camera 
geometries and the following conclusions drawn: 
i. object space precision would be critically affected by 
the image scale; 
445 
ii. optimum precision was likely to be achieved when the 
camera axes were converging to a point behind the 
cornea; 
iii. for a given image scale, small changes in the camera 
convergence would have little affect on precision; and 
iv. for the best geometry, the object space precision in X, Y 
and Z would be in the order of 15um, 151um and 20um 
respectively, leading to an r.m.s. approaching 30um. 
The design of the prototype allowed an experimental 
evaluation of the accuracy and reliability of the system for a 
selection of camera geometries. A glass sphere with a radius 
of approximately 8.5mm was manufactured and its radius 
measured to an accuracy of better than +0.5um using 
standard optical interference techniques. The™ (X.Y) 
coordinates of approximately 20 targets on the spherical 
surface were measured and corresponding Z-coordinates 
computed. Their accuracy was estimated to be better than 
Sum. Because DLT was the algorithm used in routine data 
reduction, it was used to photogrammetrically measure object 
space coordinates for the test points. The measured 
coordinates of the test points were then transformed to the 
calibration coordinate system using a least squares three 
dimensional rigid motion. Accuracy was assessed in terms of 
the residuals on this transformation. 
  
  
  
  
  
Figure 3. A cornea showing the target points marked 
onto the surface of a 10pm thick contact lens. 
Photogrammetric verification of the Keratocon indicated that 
the accuracy achieved was consistent with expectations, with 
the mean magnitude and r.m.s. of object space errors 
approaching noise levels. Within the working range of the 
instrument, predicted best precision in X and Y of 
approximately 15um (s.d.) compared with measured accuracy 
of between 3um and 10pum in X and 4um and 20pm in Y. 
Predicted best precision in Z of approximately 20um (s.d.) 
compared with measured accuracy of between 6um and18 
um. The predictions based on the formulae of Abdel-Aziz 
(1974) were therefore a useful indicator of accuracy. 
Clinical verification of the Keratocon proved to be difficult, 
primarily because there is not a more accurate method of 
measuring corneal topography and because of the difficulty 
of testing repeatability. There are two aspects of the 
instrument's clinical accuracy that still have to be quantified: 
i. It is difficult to quantify the accuracy with which the 
contact lens is representing corneal topography. A 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996