Apparatus and method for measuring the included angle of a reflective cone

An apparatus and method are provided for measuring the included angle of a reflective cone between opposite sides of the reflective cone. The apparatus includes means for illuminating the curved surface of the reflective cone with a collimated beam of light, the beam of light being generally parallel to the axis of the cone. A lens receives directly a portion of the light reflected from a first side of the cone, and focuses the portion of the light so received in a reference plane. A retro-reflective mirror arrangement, positioned on the side of the cone opposite the lens, receives directly a portion of the light reflected from a second side of the cone and redirects the light to the lens in a direction parallel to the light reflected from the second side of the cone. The second side of the cone is opposite to the first side of the cone. A light detection arrangement at the focal point of the lens displays the light received by the lens, whereby the spacing between the light received from the retro-reflective mirror arrangement and the light received directly from the cone is related to the included angle between the first and second sides of the reflective cone.

BACKGROUND OF THE INVENTION 
The present invention relates to an apparatus and method for checking a 
reflective cone and, more particularly, to such an apparatus and method in 
which the included angle between opposite sides of the curved surface of 
the reflective cone are measured. 
Reflectors in a conical shape have utility in various optical systems. Such 
a reflector has a reflective, curved surface which may be used to reflect 
a beam of light. When the beam is generally aligned with the axis of the 
cone and directed so as to strike the cone at its apex and on the curved 
surface surrounding the apex, the beam is reflected radially outward from 
the axis of the cone. If the included angle between opposite sides of the 
cone is ninety degrees, the beam is reflected radially outward in a plane. 
For example, a laser beam may thus be reflected into a plane which 
provides a continuous reference level over a construction site. 
A laser beam transmitted which utilizes a similar conical reflector is 
shown in U.S. Pat. No. 4,679,937, issued July 14, 1987, to Cain et al, and 
assigned to the assignee of the present invention. The Cain et al 
transmitter provides a conical reflector having an included angle which is 
slightly less than ninety degrees. The laser light beam travels upward, 
striking the reflector and being reflected into a slightly upwardly 
directed conical shape. This is more than compensated by refraction of a 
surrounding glass housing, however, so as to produce a cone of laser light 
which is directed slightly downward. The purpose of this slight downward 
tilt to the reference cone of light is to compensate in part for the 
curvature of the earth over relatively large construction sites. 
A principle problem which exists in the production of conical reflectors, 
regardless of the angle of the apex of such reflectors, is the difficulty 
in testing the reflectors for conformity to design specifications. This 
difficulty is due to the curved shape of the surface being measured and to 
the narrow tolerances to which reflectors must be constructed for some 
applications. It will be appreciated that if the transmitter using the 
reflector has an operating range of 1000 feet, even a very small deviation 
in the angular orientation of the reflective surface produces an 
appreciable and unacceptable error in the position of the reference light 
plane at the more remote points of the construction site. While some test 
fixtures have been developed in the past for testing conical reflectors, 
such test fixtures have been difficult to set up and time consuming to 
use. 
It is seen that there is a need, therefore, for an apparatus and method for 
measuring the included angle of a reflective cone between opposite sides 
of the cone, in which the measurement process can be effected quickly and 
accurately. 
SUMMARY OF THE INVENTION 
This need is meet by an apparatus and method according to the present 
invention for measuring the included angle of a reflective cone between 
opposite sides of the reflective cone. The apparatus includes means for 
illuminating the curved surface of the reflective cone with a collimated 
beam of light, the beam of light being generally parallel to the axis of 
the cone. A lens means receives directly a portion of the light reflected 
from a first side of the cone, and focuses the portion of the light so 
received in a reference plane. A retro-reflective means, positioned on the 
side of the cone opposite the lens means, receives directly a portion of 
the light reflected from a second side of the cone and redirects the light 
to the lens means in a direction parallel to the light reflected from the 
second side of the cone. The second side of the cone is opposite to the 
first side of the cone. A light detection means at the focal point of the 
lens means displays the light received by the lens means, whereby the 
spacing between the light received from the retro-reflective means and the 
light received directly from the cone is related to the included angle 
between the first and second sides of the reflective cone. 
The retro-reflective means may comprise a pair of mirrors having their 
mirrored surfaces oriented at a 90 degree included angle. The light 
detection means may comprise a screen. The pair of mirrors in the 
retro-reflective means may be oriented so as to reflect light received 
from the cone to the lens means along a path which is parallel to the path 
of the light received from the second side of the cone, but offset with 
respect thereto, such that the light reflected from the retro-reflective 
means to the lens means does not strike the cone. 
The light detection means at the focal point of the lens means for 
displaying the light received by the lens means may comprise a reticle 
screen in the plane. An eyepiece may be provided for viewing the reticle 
screen. The means for illuminating the curved surface of the reflective 
cone with a collimated beam of light may comprise a source of laser light. 
The included angle is equal to ninety degrees minus one half the angle of 
divergence between the light reflected by the first side of the cone and 
the light reflected from the retro-reflective means. 
The spacing in the reference plane between the light received from the 
retro-reflective means and the light received directly from the cone is 
equal to the angle of divergence multiplied by the focal length of the 
lens means. The lens means and the light detection means comprise portions 
of an auto-collimator. 
A method for measuring the included angle of a reflective cone between 
opposite, first and second sides of a reflective cone, comprise the steps 
of: 
a. illuminating the curved surface of the reflective cone with a collimated 
beam of light, the beam of light being generally parallel to the axis of 
the cone; 
b. receiving a portion of the light reflected from the second side of the 
cone and redirectng the light in a direction parallel to the light 
reflected from the second side of the cone; 
c. positioning a lens so as to focus in a reference plane a portion of the 
light reflected from a first side of the cone, and a portion of the 
redirected light from the second side of the cone; and 
d. displaying in the reference plane the light received by the lens, 
whereby the spacing between the light received from the first and second 
sides of the cone is related to the included angle. 
The step of receiving and redirecting a portion of the light reflected from 
the second side of the cone is accomplished by means of a pair of mirrors 
having their mirrored surfaces oriented at a 90 degree included angle. The 
step of displaying includes the step of displaying the light on a screen. 
The pair of mirrors are oriented so as to reflect light received from the 
cone to the lens along a path which is parallel to the path of the light 
received from the second side of the cone, but offset with respect 
thereto, such that the light reflected from the mirrors to the lens does 
not strike the cone. A reticle screen is positioned in the plane, and an 
eyepiece is provided for viewing the reticle screen. 
The collimated beam of light may comprise a beam of laser light. The 
included angle may be equal to ninety degrees minus one half the angle of 
divergence between the light reflected by the first side of the cone and 
the light reflected from the second side of the cone and subsequently 
redirected. The spacing in the reference plane between the light received 
from the first and second sides of the cone is equal to the angle of 
divergence multiplied by the focal length of the lens. The lens may form a 
portion of an auto-collimator. 
Accordingly, it is an object of the present invention to provide an 
improved apparatus and method for measuring the included angle between two 
sides of a reflective cone; to provide such an apparatus and method in 
which the measurement process is relatively insensitive to errors in the 
orientation of the reflective cone with respect to the direction of the 
illuminating collimated light beam; to provide such an apparatus and 
method in which the measurement process is relatively insensitive to 
mechanical instability of the measurement apparatus; and to provide such 
an apparatus and method in which a reflective cone may be check easily, 
simply and quickly for a desired uniform, curved, reflective surface. 
Other objects and advantages of the invention will be apparent from the 
following description, the accompanying drawing and the appended claims.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
Reference is made to the figure which illustrates apparatus constructed 
according to the present invention for measuring the included angle of a 
reflective cone 10 between opposite sides of the cone. A means for 
illuminating the curved surface of the reflective cone with a collimated 
beam of light 12, preferably a beam of laser light, includes a laser 
source 14. The beam of light 12 is generally parallel to the axis of said 
cone, indicated by dashed line 16. A lens means, including lens 18, 
receives directly a portion of the light reflected from a first side of 
conical sector 20 of the cone 10, and focuses the portion of the light 
received in a reference plane in which is positioned reticle screen 22. An 
eyepiece 24 is provided for viewing the reticle screen. The lens 18, 
reticle screen 22 and eyepiece 24 may advantageously form a part of a 
measuring telescope or an auto-collimator 25. It will be appreciated that 
the rays of light intercepted by the lens 18 diverge in a direction normal 
to the plane of the figure. As a consequence, the rays will be focused as 
a line across the reticle screen 22 which also extends generally normal to 
the plane of the figure. 
A retro-reflective means, including a pair of mirrors 26 and 28, is 
positioned on the side of the cone opposite the lens 18, for receiving 
directly a portion of the light reflected from a second side or conical 
sector 30 of the cone and redirecting the light to the lens 18. The second 
side 30 of the cone 10 is directly opposite the first side 20 of the cone. 
The pair of mirrors 26 and 28 is oriented so as to reflect light received 
from the cone 10 to the lens 18 along a path which is generally parallel 
to the path of the light received from the second side 30 of the cone, but 
offset with respect thereto, such that the light reflected from the 
retro-reflective means to the lens does not strike the cone. 
The light rays traveling from the mirror 28 to the lens 18 have directional 
components in the plane of the figure which are parallel to the 
directional components in the plane of the figure of these rays as they 
travel from side 30 of cone 10 to mirror 26. The mirrors 26 and 28 have 
their mirrored surfaces 32 and 34, respectively, oriented at a ninety 
degree included angle so as to provide retro-reflection. 
It will be appreciated that the mirror 26 intercepts diverging rays which 
are reflected from the curved reflective surface of the cone 10. The 
divergence of the rays in a direction normal to the plane of the figure 
continues as the rays are relfected by the mirrors 26 and 28 and travel to 
the lens 18. The mirrors provide retro-reflection of the rays of light in 
the plane of the figure, a plane which is normal to the reflective 
surfaces 32 and 34. Like the rays of light intercepted by the lens 18 from 
side 20, the rays of light received by lens 18 from mirror 28 diverge in a 
direction normal to the plane of the figure. As a consequence, these rays 
will also be focused as a line across the reticle screen 22 which extends 
generally normal to the plane of the figure. 
The reticle screen 22 provides a light detection means at the focal point 
of the lens 18 for displaying the light received by the lens. It has been 
found that the spacing between the light received from the 
retro-reflective mirrors 26 and 28 and the light received directly from 
the side 20 of cone 10 is related to the included angle between the first 
and second sides 20 and 30 of the reflective cone 10. The included angle 
is equal to ninety degrees minus one half the angle of divergence between 
the light reflected by the first side of the cone and the light reflected 
from the retro-reflective means. Thus, if the rays 26 and 38 diverge in 
the plane of the figure by 1 degree, the included angle is measured as 
89.5 degrees. Similarly, if rays 26 and 28 converge in the plane of the 
figure by 1 degree, the included angle is measured as 90.5 degrees. 
The spacing in the reference plane defined by the reticle screen 22 between 
the light received from the retro-reflective mirrors 26 and 28 and the 
light received directly from the cone 10 is equal to the angle of 
divergence or convergence multiplied by the focal length of the lens 18. 
As a consequence, by merely observing the screen 22 through the eyepiece 
24, a measurement may be made which permits ready calculation of the 
included angle of the cone. If there is a question as to whether the rays 
36 or 38 are converging or diverging, one may simply block off one of the 
two light paths momentarily so as to identify the source of the lines of 
light which are focused on the screen 22. 
It will be appreciated that if retro-reflective mirrors 26 and 38 are 
oriented at other than a 90.degree. angle, the light rays traveling from 
mirror 28 to the lens 18 will have directional components in the plane of 
the figure which are not precisely parallel to the directional components 
in the plane of the figure of these rays as they travel from side 30 of 
cone 10 to mirror 26. This is acceptable, provided an appropriate 
correction is made in the angle measured by means of lens 18 and reticle 
22. 
It has been found that the apparatus and method of the present invention 
provide a simple and reliable way of measuring the included angle of a 
reflective cone. This approach is relatively insensitive to alignment of 
the cone with respect to the test apparatus. If the cone is tipped 
slightly out of its desired orientation, the result is a slight movement 
of the lines of light on reticle screen 22. Since both lines move together 
with the distance between them remaining constant, however, the 
measurement process is unaffected. It will be appreciated that the cone 10 
may be rotated about its axis 16 and additional measurements made. This 
may be facilitated, if desired, by providing a rotary support for the 
cone. 
Having described the invention in detail and by reference to the preferred 
embodiment thereof, it will be apparent that modifications and variations 
are possible without departing from the scope of the invention defined in 
the appended claims.