# Aligning reflecting optics with Bessel beams

ABSTRACT

Bessel beams have found use in the alignment of transmissive optics for some time. They are also used for the alignment of reflecting optics when used in the imaging mode, that is, when the wavefront is near spherical. However, there are cases where it would be useful to use the Bessel beam for alignment of far-off axis aspheres to order to get the asphere aligned close enough to its final position that light will go through the system in the imaging mode. In another mode, the Bessel beam is used to determine the normal to a free form surface.

# Alignment of Optical Systems

1. Introduction

As optical systems become more complex and packaging requirements more severe and multi-dimensional, proper alignment becomes more challenging. Yet with current improvements in the manufacture and measurement of optical surfaces to nm levels, alignment is one of the few remaining opto-mechanical aspects of optical system manufacture and assembly where improvement in optical performance can be made. There are four approaches to aligning optical systems. These will be described and the advocated method illustrated by examples.

The preferred alignment method overcomes most of the difficulties of traditional methods but requires a new way of thinking about alignment. The method also requires alignment considerations must be studied immediately after the optical design is complete so that the necessary opto-mechanical datums can be incorporated into the mechanical design of the optical system cell, chassis or lens bench.

# Calculation of the Vertex Radius of an Off Axis Parabolic Surface using the Sag Measured with a Three Ball Spherometer

Abstract

We describe a method of calculating the vertex radius of an off-axis parabolic segment using a three ball spherometer to measure the sag. The vertex radius is found by solving a set of six simultaneous, non-linear equations for the three coordinates of one of the ball centers and the corresponding three coordinates of the point of tangency of the ball with the surface.

# Centering Steep Aspheric Surfaces

### 1. INTRODUCTION

Finding the optical axis of an aspheric surface is an essential part of making an aspheric lens because the center of curvature, or optical axis, of the second side must lie on, or be coincident with, respectively, the optical axis of the first side for maximum optical performance. Looking at the center of an aspheric surface and measuring the tilt and coma as a function of decenter is an obvious means of determining centration, but many aspheric surfaces are relatively spherical over the part of the lens aperture that can be viewed with commercially available optics and there is too little coma to make a useful measurement of decenter.

We describe an alternative method of viewing a small patch of the aspheric surface near the edge of the clear aperture where the asphericity is greatest while rotating the lens about an axis close to coincident with the optical axis of the surface. By also tracking the reflected light image when using an autostigmatic microscope (ASM), or using an interferometer to measure the low order Zernike coefficients, as the lens is rotated, both the tilt and decenter of the surface can be determined.

The relationship between the image motion and Zernike coefficients is described for both tilt and decenter of the surface as well as the means of separating the relative amounts of tilt and decenter are given. These methods of determining tilt and decenter seem to work for all aspheric surfaces we have tried to date.

We begin by reviewing the thinking that led to the method described for finding the optical axis of an aspheric surface. The discussion moves through successive attempts to find a method of locating the optical axis for aspheric surfaces that works for all surfaces that have enough asphericity to qualify as aspheres. Results are shown for both the interferometer and the autostigmatic microscope method*. Finally, we conclude by describing a method that may work even better for many aspheric lenses that makes use of a computer generated hologram.

*After submitting the Abstract for this talk it came to the author’s attention that there is a European Patent #EP 1918 787 A1 covering the autostigmatic microscope method described in this paper for locating the optical axis of the first surface of an aspheric lens.

# Computer Generated Holograms as Fixtures for Testing Optical Elements

### 1. Introduction

It is common to think of computer generated holograms (CGH) as artifacts for testing aspheres but they can also be used as general calibration artifacts and fixtures for the alignment and test other more conventional optics. We show how simple Fresnel zone patterns can be created to simulate centers of curvature or axes in space with dimensional precision associated with microlithography. These centers of curvature and axes can then be located in space to similar sorts of precision with an autostigmatic microscope (ASM) or an interferometer.

Once the ASM is centered on the center of curvature, or axis, of the Fresnal zone pattern, a ball, or cylinder, respectively, of matching radius can be aligned to the ASM or interferometer to similar sorts of precision and physically attached to the CGH to serve as kinematic datums against or on which to mount other optical or mechanical components.

We then give an example of the fixture for the mounting of a rectangular lens element into a kinematically located frame so the two can be cemented together prior to inserting the bonded pair into an optical bench.

# Conjugate Selection for Precision Lens Centering

ABSTRACT

The concept of centering a precision, symmetric lens system using a high-quality rotary table and an auto-focusing test instrument are well known. Less well known are methods of finding convenient, or easily accessible, lens conjugates on which to focus while performing the centering operation. We introduce methods of finding suitable conjugates and centering configurations that lend themselves to practical centering solutions.

# Design for Alignment

### 1. INTRODUCTION

The premise of this paper is that the only remaining way to improve optical system performance is with better alignment techniques. We feel optical design is a mature field and that little can be done to improve the design of optical systems by improvements to lens design software. The software may become easier or more convenient to use but the optical designs produced are near optimum given the design constraints specifying the system.

The same holds for the manufacture of optical elements. Between computer controlled manufacturing methods and interferometric testing of the manufactured elements and the many improvements in optical glass quality, not many avenues are open to improved quality of the optical components themselves. The only area left for improvement in performance of precision, or high quality, optical systems is the assembly and alignment of the glass elements and mirrors into mechanical cells, and lens benches, for more complex system geometries.

Based on this premise we will first define our concept of what precision optical alignment means and why traditional methods of alignment have not kept up with the improvements in lens design and the manufacture of high quality optical elements. We contrast traditional methods with more modern methods of optical alignment that make use of optical datums rather than mechanical datums and show the advantages of the optical methods.

Next, we show some advances in the optical methods of alignment including newer optical alignment tools and tooling including gratings that define axes in 5 degrees of freedom and how these make alignment easier. Finally, we look at the implications of these newer methods on how the opto-mechanics of cell and lens bench design are impacted so that tolerances can be loosened while achieving improved optical system performance. While this applies largely to precision optics manufacture, there are aspects of this approach that are applicable to production assembly as well.

# Lens Centering Using the Point Source Microscope

ABSTRACT

Precision lens centering is necessary to obtain the maximum performance from a centered lens system. A technique to achieve precision centering is presented that incorporates the simultaneous viewing through the upper lens surface of the centers of curvature of each element as it is assembled in a lens barrel. This permits the alignment of the optical axis of each element on the axis of a precision rotary table which is taken as the axis of the assembly.

# Method of Alignment using a Laser Tracker System

1. Introduction: Laser trackers are an accurate and efficient tool for finding the locations of features in a threedimensional space but they rely on Spherically Mounted Retroreflectors (SMR) to return the laser beam to the tracker. If the feature cannot be contacted or it is not convenient to use an SMR another method must be used to follow the beam. We describe methods using a dual imaging and autostigmatic microscope for locating the features and two methods for tracking the microscope location depending on the type of tracker used. This converts a contact probe, large area CMM into a non-contact CMM by coupling a laser tracker with a dual purpose autostigmatic microscope. We begin with a brief description of the microscope followed by the alignment of the microscope to tracking and scanning laser metrology stations.

# Non-Contact Probe for On-Machine Metrology

INTRODUCTION
On-machine metrology is particularly important for diamond turning and grinding as it is difficult to remount and align a part if it does not meet off-line inspection criteria. There is also the issue of tool wear; a process that started well may fail part way through the cut, and if tool replacement is needed, it is vital to know that before removing the part. A means of rapid, noncontact, in situ profiling and roughness measurement could improve the productivity of diamond tool machining.

Recently we first showed that diamond turning machines are sufficiently isolated that steady fringes can be obtained by simply setting a Point Source Microscope [1,2] equipped with an interferometric Mirau objective on the cross slide of a machine. Further, we demonstrated that the machine can be precisely driven to get temporally shifted fringes so that common algorithms can be used to obtain area based surface roughness measurements. This led to the question of whether essentially the same hardware could be used to rapidly profile diamond turned parts. We show via simulation that the answer is yes and that the approach can be implemented rather simply.

We first describe the PSM and its configuration as a Microfinish Topographer (MFT) by using interferometric data reduction software. Then we describe how this hardware is changed into a profiler by changing the light source and camera. Finally, we show how this hardware that we call a Non-Contact Profiler [3] (NCP) is used on a diamond turning machine to profile turned or ground parts in situ.

# Optical Alignment Using the Point Source Microscope

ABSTRACT

We give an example of a Point Source Microscope (PSM) and describe its uses as an aid in the alignment of optical systems including the referencing of optical to mechanical datums. The PSM is a small package (about 100x150x30 mm), including a point source of light, beam splitter, microscope objective and digital CCD camera to detect the reflected light spot. A software package in conjunction with a computer video display locates the return image in three degrees of freedom relative to an electronic spatial reference point. The PSM also includes a Köhler illumination source so it may be used as a portable microscope for ordinary imaging and the microscope can be zoomed under computer control. For added convenience, the laser diode point source can be made quite bright to facilitate initial alignment under typical laboratory lighting conditions. The PSM is particularly useful in aligning optical systems that do not have circular symmetry or are distributed in space such as off-axis systems. The PSM is also useful for referencing the centers of curvatures of optical surfaces to mechanical datums of the structure in which the optics are mounted. By removing the microscope objective the PSM can be used as an electronic autocollimator because of the infinite conjugate optical design.

### Case Studies & Testimonials

• Sometimes good news goes unnoticed for the longest time. We just stumbled on this unattributed, but complimentary note about the PSM.

Notice the PSM in the top center of Fig. 9.  Optical Perspectives Group would like to express "thank you, IDEX".

• ### "We are enjoying our Point Source Microscope and finding it invaluable in alignment and diagnostic tasks."

Dr. John Mitchell
Senior Optical Metrologist
Glyndwr Innovations Ltd., St. Asaph, Wales, UK

• ### "Just wanted to share a recent success aligning an adaptive optics test bed with the PSM. We used to use a traditional alignment telescope in the past, but the PSM made the whole process really easy and fast. The main requirements were to quickly determine the quality of beam collimation and pupil conjugates since there are several beam expanders and compressors with multiple pupil and focal planes."

Suresh Sivanandam
Dunlap Institute for Astronomy and Astrophysics
University of Toronto

• ### "You are always responsive and give us lots of useful information!!"

Dr. Shaojie Chen
Dunlap Institute for Astronomy and Astrophysics
University of Toronto

• ### "As always we are very much loving the instrument, I personally love the camera upgrade from what I'm used to!"

Weslin Pullen
Hart Scientific Consulting International, LLC
Tucson, Arizona

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