DESIGN OF A REFLECTION APPARATUS FOR LASER BEAM PROFILE MEASUREMENTS* Eric G. Johnson, Jr. Measurement of both the irradiance and phase front (the beam profile) in real time from the output of a laser has interest for control of that beam and for efficient energy and economic design of the source and the resulting optical systems. The National Bureau of Standards (NBS) has begun a program to build a unit that can measure, at numerous wavelengths from 1.06 μm to 10.6 μm, a selected spatial sample of the beam profile. This device would have the following features: (1) The different carrier wavelengths use the same apparatus by changing two mirrors. (2) The beam profile is sampled simultaneously with no time-shift distortions. (3) The output data streams documenting the sampled beam profile are continuous and are distorted only by the finite number and the time constants of the detectors. (4) The phase-front information is generated before the detectors create the data (5) The apparatus uses mirrors and a reflection hologram that is computer generated. (6) The unit is calibrated piecewise over the range of relative phase and irradiances for each pair of neighboring sampling holes which are 5 mm apart. (7) The resulting calibrated unit can measure profiles near 10 cm in diameter with phase-front variations of less than 5 wavelengths. (8) The expected response time for measurements as controlled by the electronics is of the order of several tens of nanoseconds. The design analysis reported here includes: (1) the theory which uses Fourier optics concepts with off-axis reflections and rough surfaces to provide the basis for accurate computer simulation of laser beams; (2) the program, BEAM, which generates the expected behavior of the apparatus under variation of laser wavelength, physical dimensions for curvatures, hologram structure, and changes in positions of the various components; (3) the simulation results which demonstrate the expected characteristics for the apparatus; and (4) the key element in the apparatus, namely the reflection hologram, which requires discussion of the design, construction, and testing of this element. The Hartmann plate method is described briefly so that a comparison between it and the holographic method can be made. The comparison shows why the holographic method is best for a standard for irradiance and phase-front measurements. Key words: Beam profile; calibrated system; holography; irradiance; laser diagnostics; phase front. INTRODUCTION A previous publication [1] has documented the background for beam profile measurements and has indicated the basis of the holographic method. Here we develop the design details for a reflection system. This technical note presents sequentially the concepts and results necessary to estimate for selected accuracy the allowed range of irradiance levels and phase-front variation for an apparatus using the holographic method. This presentation format has been chosen to give the reader the option either for scanning each section for a sense of the design or for studying the analysis in detail in order to construct a similar apparatus. *Funded in part by the Calibration Coordination Group (CCG) under contract No. 78-109. The design development, grouped as nine sections, begins in section 2 with a general description of the apparatus and an operation synopsis. The remaining sections detail, in turn, particular points of the design process. We indicate those points below--one for each paragraph. In section 3, we derive the necessary improvements to the scalar theory for coherent wave propagation under the Fourier optics approximation with due consideration for the surface character of the mirrors and the hologram and for the effects due to off-axis illumination of these optics. In section 4, we describe the computer program generated from these corrected formulas so the reader can copy y and use this program. This program allows a reader to simulate the apparatus before construction. There are numerous adjustment parameters for a given apparatus. It is impossible to select the correct version; rather, we arbitrarily select certain convenient choices and then adjust the remaining parameters to make the design as accurate as possible. In section 5, with the computer program as given, we apply this capability to study one possible configuration for the 10.6 μm wavelength. Here we select the arbitrary parameters and adjust the remaining parameters to get the optimum system. The numerous quantitative results show what can happen. These results range from alignment with an HeNe laser to sensitivity studies from variation of parameters such as wavelength, equipment dimensions, and curvatures of the mirrors. Because the apparatus is expected to be used at wavelengths in addition to 10.6 μm and because 1.06 μm has significant use, in section 6 we repeat the process described in the previous section for 1.06 μm wavelength. These results should give the designer a clear picture of how to use the holographic method over a range of wavelengths. Because these simulations have developed large blocks of apparently unrelated information, in section 7 we extract key results from sections 5 and 6 to establish a pictorial sense for the ideal operations, given these results. Additional simulations are performed here to drive home the capabilities and limits of this apparatus. Normally in construction of a complex apparatus, there is great interest in the electronics of the device. Here the action of the optics on the laser radiation is more important; therefore, in section 8 we present the details for the surface hologram. This item is a key optical component for successful operation of the apparatus. We discuss the ideal concepts and the practical limitations such as allowed variation of the carrier frequency (wavelength), beam splitting efficiencies, and implications about the ultimate accuracies of the apparatus for beam profile measurements. To complete the design, we indicate the equipment that can be bought and its approximate cost. Section 9 contains specifications for the equipment. We identify the necessary custom machining for the apparatus. The section also contains a summary on the detector unit which must be custom built. In subsection 9.3 we define some options for construction of the detector unit. In section 10, we conclude the design phase for the reflection unit by summarizing the estimated cost for construction of the apparatus and by discussing other bottom line issues such as what is the expected accuracy of the device and why the unit is the best system for a standard of beam profile measurements compared with other techniques. To provide a clear comparison between the holographic and the Hartmann plate methods, we briefly describe in the appendix what the Hartmann plate unit would do for the same design conditions as already detailed for the holographic method. 2. AN OVERVIEW OF THE BASIC APPARATUS We define the reflection apparatus using the background terminology and concepts described in technical note [1] as a basis for the discussion in this section. In figure 2.1, a block diagram indicates the key optical stages for the unit. We describe the actions of each stage going from the prefilter to the array of detectors in the cross-correlation plane. The construction details and technical limits of the apparatus are relegated to section 9 and its subsections. The details of the hologram are in section 8. The prefilter has an array of holes with a beam sampling pattern as shown in figure 2.2. The field of view of the apparatus is fixed as a circle 10 cm in diameter. Each hole spatially samples the incident radiation to get a laser beam, 1 mm in diameter, which then undulates through the apparatus. To visualize the action by each stage of the apparatus, we trace in the paragraphs below what happens to one beam, exiting from an arbitrary hole in the prefilter. The prefilter is located at approximately one focal length (mirror 1) in front of the first Fourier transform mirror. The beam from a single hole in the prefilter becomes an Airy pattern with a flat phase front at approximately one focal length (mirror 1) after the reflection off this mirror. The magnifying telescope has two mirrors which correctly scale this Airy pattern. to the reflection pattern on the hologram. Mirror 2 has its radii of curvature changed to match the wavelength of the incident radiation. The nominal position of this mirror is one focal length (mirror 2) after the Fourier plane of mirror 1. The position of mirror 3 is one focal length (mirror 2) plus one focal length (mirror 3) after the mirror 2. The properly matched Airy pattern, again with a flat phase front, at the hologram is approximately one focal length (mirror 3) after mirror 3. The surface hologram splits each Airy pattern into a single reflected beam plus eight diffracted beams exiting in a square array all of which diverge around the reflected beam. The Fourier transform done by mirror 4, located one focal length (mirror 4) after the hologram, causes the resulting nine beams to form a three-by-three array of spots in the Fourier plane of mirror 4, namely one focal length (mirror 4) after this mirror. Because the detector array has physical constraints that will prevent a match to the pattern at this last Fourier transform, mirror 5 magnifies and images the resulting spot pattern onto a detector array at the cross-correlation plane. Figure 2.3 shows the expected pattern when all holes in the prefilter are illuminated and the wavelength of the carrier frequency is properly matched to the curvatures of the five mirrors. The detector array has a detector at each spot that has only one or two beams contributing to the irradiance on the detector. If maximum accuracy in real time is needed, then there are detectors at the spots which have four-beams contributing to the irradiance at that spot. (At this stage, all phase-front details can be ignored.) Each detector measures the resulting laser power in its intersected spot to produce electrical signals. These signals represent the needed information about the original beam profile at the prefilter plane once the apparatus has been calibrated properly (see [1]). |