Wastig Pe ATgp2 cos2 e 2 141

Here is the coefficient giving the amplitude of the astigmatism, p is the distance from the axis, and 8 is the angle from the axis of astigmatism. The constant XA subtracted from the cos2 8 term is the needed focus shift to produce a Zernike best-focus aberration. Below, the astigmatism axis is conveniently placed at 0 , but it can occur at any angle. Wastig is graphed in Fig. 14-2. For example, if AaUg is wavelength, then W . goes from +78 wavelength to 78 wavelength. This definition is...

Spherical Aberration

The most common error on the glass is called spherical aberration. It resides to some degree on all surfaces and need not become debilitating, though that depends on its severity. The star test for spherical aberration is surprisingly sensitive and easy to interpret. This chapter will make five points 1. Wavefronts deformed by simple spherical aberration (fourth-order curves) are recognizable by noticing that light approximately follows the behavior of the ray-optics caustic. On one side of...

Telescopes Are Filters

The telescope is a device that reproduces an image of reality. It does not write on paper like a copy machine, but its images are just as unreal. It creates its reproduction on a tiny image plane only a few centimeters from the tip of the observer's nose. The scrutiny is done using a powerful magnifying lens called an eyepiece. Only through the multiplicity of imaged values (location, color, brightness) and the selective visual processing power of the human brain does this reproduction get...

Aligning Three Telescopes

The alignment procedure for every commercial telescope cannot possibly be described because each maker has tiny variations in the manufacture of cells, mirror holders, and adjustment hardware. For this reason, we will examine the generic features of the process used in aligning only three common telescopes. In spite of this restriction, the descriptions which follow represent a large number of optical systems. You will not be given detailed instructions in the form of a recipe to be learned by...

Performing the Test

Because people wanting to test telescopes don't usually have access to towers or convenient topography to elevate the sphere, they must test through ground turbulence. Daytime testing is probably best done during the early morning and over a grassy field, but different locations and times have their own behavior. Often, a quiet time of non-turbulent behavior can be found to briefly persist near sunset. Go ahead and try the test anytime and anywhere you may be pleasantly surprised. Also, try to...

Other Tests

The 1930s were boom years for amateur telescope making in the United States, primarily through the popularization efforts of individuals such as Russell Porter and Albert Ingalls. Estimates have been made that up to 250,000 telescopes were begun during the years before World War II. In a way, it was the only option. The Great Depression was raging, and established optical shops specialized in making expensive refractors or contracting for professional instruments. If you wanted a reasonably...

Air Turbulence and Tube Currents

Some sources of aberration have nothing to do with the telescope itself. They come from the necessary immersion of the instrument in a changing optical medium. The light of astronomical objects must traverse a turbulent column of air that extends many kilometers from the top of the atmosphere to the focal plane of the instrument. Little can be done by the amateur observer about turbulence high in the atmosphere, but it is easy to recognize in the star test. Many of the problems described in...

N

For f 6 optics with a 100 line inch grating, taking as the wavelength the yellow-green color that the human eye likes best, the maximum tolerable distortion with 2.5 lines showing is about 0.04. Anyone who has ever used one of these gratings knows that the sharpness of Fig. A-6 present an unrealistic view of what is happening. The actual shadows are fuzzy and indistinct. A 4 bowing of the lines in the presence of this fuzziness is nearly impossible to see. Figure A-8 depicts the actual pattern...

An Abbreviated Star Test Manual

You will need a high magnification eyepiece to conduct the star test successfully. The exact power varies from telescope to telescope and depends on what you are trying to see, but it is around 10 per centimeter of aperture. For a common 20 cm Schmidt-Cassegrain telescope, magnification should equal 20 x 10 200. Since the focal length of such an instrument is 2 meters, the eyepiece focal length should be around 10 mm. Low focal-ratio instruments are not evaluated to the same degree of precision...

Obstruction and Shading

Modifying the transmission of the aperture pupil causes changes to the diffraction pattern. Obstruction and shaded transmission are not deformations of the wavefront in the same sense as aberrations. They can occur in officially perfect apertures. Nevertheless, they can affect the perceived image quality in a very similar manner. Five main points are made in this chapter 1 Central obstructions below 20 of the aperture are indistinguishable in practice from an unobstructed aperture, and for...

IS e2naRMS 2132

It gives a more accurate number than Eq. 13.1 at large aberration amplitudes. We can invert Eq. 13.2 for a iS 0.8 to define a Mahajan tolerance of about 713 wavelength RMS. For small roughnesses, however, the difference between these approximations is negligible. We must distinguish the nomenclature from the reality of surface error. Roughness is typically modeled either as a continuous spectrum from large scale to small scale or as a discontinuous composite scale spectrum. The spectrum in this...

Accumulated Optical Problems

Spherical Aberration Central Obstruction

What you have been shown thus far is how the individual aberrations and transmission variations can affect the image. More important, however, is the way minor problems add up. The wobbly stack of Fig. 3-1 shows how many errors accumulate as a collection of filters. Even if each filter is relatively unimportant, the total filtration could render the image fuzzy and indistinct. The concept of modulation transfer outlined in Chapter 3 presented a single standard around which we could rally. By...

Table of Contents

An Introduction to the Author xi 1.1 Telescope 1.2 Testing the 1.2.1 Sources of 1.2.2 Measures of Optical 1.3 The Star Test A Brief 1.3.1 Diffraction 1.4 The Reason for Star 2 An Abbreviated Star-Test Manual 17 2.1 Some Necessary 2.2 Optical Problems in 2.2.1 Secondary Mirror Obstruction 2.2.3 Atmospheric Motion and 2.2.4 Tube 2.2.5 Pinched or Deformed Optics 2.2.6 Spherical 2.2.7 Rough 2.2.8 Zonal 2.2.9 Turned 2.2.10 Astigmatism 2.3 Concluding 3 Telescopes Are Filters 35 3.1 Perceptions of 3.2...

Circular Zones and Turned Edges

This chapter discusses zonal defects and a common type of zonal error, a turned edge. It will make four chief points 1 On mirrors of amateur size, interior zones are seldom large enough to be troublesome. 2. Zonal defects can be detected by defocusing a larger amount than is usual. 3 Turned edge is a persistent problem that yields contrasts worse than the smaller aperture inside the turned annulus. 4. Narrow turned edges can be treated by masking or painting the edge. Zones are slight circular...

Nodes and Antinodes

Certain locations in the volume around the brightest image point appear to be dark compared with their immediate surroundings. Figures 4-7 and 4-8 showed two such points on the first and second dark rings. In defocusing, on-axis darkness is found when the number of Fresnel zones is an even number. These locations appear to be quiet while the tumult rages around them. They are nulls, more commonly called nodes. The opposite of a node is an antinode, where the wave action is strongest and the...

Spherical Aberration N Telescope

Star Test Newtonian

Focused patterns for 0, 1 8, 1 4,1 3,1 2, and 1.7 wavelengths of lower-order spherical aberration. The aperture is unobstructed. a) normal, OB 33 b) SA -1 8 7 a) normal, OB 33 b) SA -1 8 7 Fig. 10-8. In-focus patterns for a) 0, b) 1 8, c) 1 4, d) 1 3, e) 1 2, and f) 1.7 wavelengths of lower-order spherical aberration. Aperture has a 33 centered circular obstruction. Fig. 10-8. In-focus patterns for a) 0, b) 1 8, c) 1 4, d) 1 3, e) 1 2, and f) 1.7 wavelengths of lower-order spherical...

Pinched and Deformed Optics

Star Test Newtonian

At the start of each observing session, you should star test for problems that may change with transport of the telescope or a remounting of the optics after maintenance. This chapter will discuss the star-test pattern characteristic of one such warping and will present ways to relieve unusual stresses on the optics. Beyond the image improvements derived by giving careful attention to the deformations, you may be able to avoid catastrophic damage. Edge fractures are common among mirrors with...

La4ra1

Where R is the approximate radius of curvature of the mirror and D is its diameter. LA means longitudinal aberration, the stretch of the black bar in the diagram. For a hyperboloid, LA is a larger number, and for a prolate spheroid it is smaller. If an optical worker measures the shift between situations A and C and keeps changing the shape of the mirror until that shift is at or a little less than D2 4R, then the paraboloid is closely approximated. Before Foucault, mirror making had been the...

Effects of Misalignment

If alignment isn't precise, any number of bad effects can result. Although we will calculate patterns only for misaligned Newtonian reflectors, the behavior depicted here qualitatively describes a wide variety of systems and is generally useful. Off-axis, a Newtonian reflector exhibits a mixture of two pure aberrations, coma and astigmatism. In this case, astigmatism isn't ground into the glass permanently. It is caused by viewing the mirror at an oblique angle. Similarly, coma is induced...