Measurement of Centering Errors

The following sections describe the measurement principle behind the OptiCentric^® instruments and typical errors which occur during the assembly of lenses and objectives. The measurement of a centering error primarily involves defining a point of symmetry in relation to a reference axis. This can, for example, be the center of curvature of a lens surface or the location of a focus point of a lens in relation to a reference axis. When the center of curvature of a lens surfaces is used for measurement of centration errors, the measuring procedure is known as “Reflection Mode”. Similarly the measuring procedure using the focal point of a lens is known as “Transmission Mode”

Principle of the Centering Error Measurement in Reflection and Transmission Mode

The basic procedure to identify the centering errors of a lens implies the rotation of the lens around a precise reference axis. The precise reference axis is decisive for the accuracy of the measurement. The OptiCentric^® product line provides different instrument modules or accessories featuring an extreme accurate reference axis for the measurement.

For the measurement, an autocollimator with additional optics is focussed either in the center of curvature of the surface (Reflection Mode) or in the focal plane of the lens (Transmission Mode). For the measurement in transmission a collimator is additionally needed. The parallel beam emerging from the collimator is focussed in the focal plane of the sample to be measured.

The images reflected from the lens surfaces (Reflection method) as well as the images projected into the focus of the lens (Transmission Method) are observed through the eyepiece of an autocollimator of a telescope or of a microscope.

In the modern instruments the autocollimator is equipped with a CCD-Camera and the entire measurement process is controlled by the software.

When a centration error is present, the observed image describes a circle while the sample is rotated around a reference or datum axis. When using software programs the rotation of center of curvature can be followed directly on the monitor. The live reticule image shows the exact position of the center of curvature in the x-y plane, whereby the center of the circular path represents the reference axis.

The radius or the diameter of the circle is proportional to the size of the centring errors. The result of the measurement can be given as radius of the run out circle (in μm) or as tilt of the surface or of the lens axis (in arcsec).

Comparison between Reflection and Transmission Mode

Transmission and reflection measurements essentially provide different results. The reflection measurement will provide exact information on the centering error of single surfaces, while the transmission measurement provides an “overall error” which is a combined result of the centering errors of all the single surfaces.

In transmission mode it is not possible to determine which one of the two surfaces of a lens is producing the centration error. In some cases, a lens tested in transmission mode can reveal no centering error, although the lens is tilted in the mount.

The images reflected from the lens surfaces, however represent an undoubted criterion for the surface tilt and the individual centring errors. The reflection method is the only total and true method for the measurement of centration errors. However, the reflection method is in many cases difficult to manage. On the other hand, the transmission method with some mechanical constraints gives in many cases satisfactory results. For a good economy of the optical manufacturing both methods should be considered. OptiCentric^® allows both methods to be used.

The reflection and the transmission values are therefore different and may only be compared to a limited extent. A simple relationship between the two measurements for the centering error of a single lens only (without a mount) can be given by:

T = (n - 1) R

R: Surface tilt error of top surface (Result of measurement in reflection mode)
T: Angle deviation in transmission mode
n: Refractive Index of glass

Centering Errors of Lenses

Centering errors have a decisive influence on the optical imaging quality of an imaging system. A centering error is present if the axis of symmetry of an optical element does not coincide with a given reference axis. The reference axis is typically the symmetry axis of a mount or cell. The centering error is given as an angle between the optical axis of this element and the reference axis. A centering error may also be given as the distance between, for example, a center of curvature and another reference point on the reference axis.

Fig. 3 provides an overview of the typical centering errors.

1. Translational displacement of a lens
2. Tilt of a lens
3. Surface tilt error of a spherical surface
4. Cementing error
5. Tilt of the aspherical axis

OptiCentric^® is able to define precisely all of these errors in accordance with ISO 10110-6. OptiCentric^® features capabilities for measuring single lenses, surface tilt and cementing error or for the measurement of complete objectives. The so-called MultiLens^® procedure enables the measurement of the centering error of all single surfaces of a fully assembled objective without the need to dismantle it. Building on this comprehensive measurement function, systems have been developed to carry out the precise assembly of optical systems as an extension of the OptiCentric^® system.

The Centering Error of a Spherical Surface

The centering error of a spherical surface is defined by the distance “a„ of its center of curvature “C1„ to a reference axis. The surface tilt error χ may also be used.

The following correlation applies (r = radius of the surface under test):

χ = arcsin (a/r) [rad]

χ_D = 3438 χ [arc minutes]
χ_D = angle of the centering error in arc minutes

It is also possible to provide the measured surface tilt error as eccentricity S at the lens edge if required. (Fig. 5)

S = D X tan(χ)
D = lens diameter

The Centering Error of a Lens

The optical axis of a single lens (see figure 6, left side) is the line connecting the centers of curvature of the two spherical surfaces. The centering error is now defined using the angle „χ“ and the distance „a“ to a given reference axis.

If only a single lens is being defined, then the relationship between the centering error and the processing of the lens edge is important. In this instance, the reference axis used is a line through one of the centers of curvature and the center of the diameter (see figure 6 right side). The surface tilt error of the second surface is given in relation to this tilt axis. This error is also known as the wedge error of a lens.

Centering Errors of Aspherical Lenses

In contrast to spheres, defined by a center of curvature, aspherical surfaces have an axis of symmetry. Therefore, in order to define a centering error at least one distance information is required in addition to an angle.

The angle is defined by the angle between the aspherical axis and the reference axis. The distance may only be defined for one specific reference point on the reference axis. This could be the center of curvature in the paraxial area of the asphere, for example.

The following parameters are measured by the OptiCentric^® program:

1. Shift and tilt of the asphere axis in relation to the reference axis of rotation.
2. Shift and tilt of the asphere axis in relation to the optical axis of the lens. The “optical axis” is considered to be the line running through the centers of curvatures of the spherical portions.
3. When a lens consists of two aspherical surfaces the angle and shift of both aspherical axes are determined.

Centering Errors of Cylindrical Lenses

A cylindrical surface has an axis of symmetry, called the cylinder axis. There are different centering errors related to the cylinder axis.

1. Angle between the cylinder axis and the edge of the lens
2. Offset of the cylinder axis to the edge of the lens.
3. Angle between the cylinder axis and the plane surface of the lens.

The OptiCentric^® system is also able to define the centering error of the cylinder axis in assembled anamorphic objectives.

Centering Errors of Optical Surfaces within an Assembled Objective

In order to measure single optical surfaces, the exact tilt error and/or exact position of the center of curvature to a given reference axis has to be determined. Influences from optical surfaces and elements located before the surface under test are taken into account using optical calculations including the centering error of these surfaces. That means that the centering error of all further surfaces must be iterated from that of the first.

Approx. 20 surfaces can be measured from one side using this method. If a second measuring head is used, such as in the OptiCentric^® MOT Dual, which calculates the centering error from the bottom side, up to 40 or more optical surfaces can be measured.

For this application a special software module MultiLens^® has been developed. The MultiLens^® measurement provides the exact x,y,z co-ordinates of all centers of curvature in the space. The measured data support further analysis of the lens system and provide additionally the following data:

• Calculation of the optical axis of any single lens of the system.
• Assessment of the optical axis of single subsystems or the entire optical system. A „best fit“ line is drawn through all the optical surfaces under consideration.