Celestron CGX Equatorial 800 HD Telescopes Whitepaper EdgeHD Optics - Page 6

4. OPTICAL PERFORMANCE OF THE EDGEHD Optical design involves complex trade-offs between optical performance, mechanical tolerances, cost, manufacturability, and customer needs. In designing the EdgeHD, we prioritized optical performance first: the instrument would be diffraction-limited on axis, it would be entirely coma-free, and the field would be flat to the very edge. (Indeed, the name EdgeHD derives from our edge-of-field requirements.) Figure 2 shows ray-traced spot diagrams for the 14-inch aperture classic SCT, coma-free SCT, and EdgeHD. All three are 14-inch aperture telescopes. We used ZEMAX® professional optical ray-trace software to design the EdgeHD and produce these ray-trace data for you. Each spot pattern combines spots at three wavelengths: red (0.656µm), green (0.546µm), and blue (0.486µm) for five field positions: on-axis, 5mm, 10mm, 15mm, and 20mm off-axis distance. The field of view portrayed has diameter of 40mm- just under the full 42mm image circle of the EdgeHD-and the wavelengths span the range seen by the dark-adapted human eye and the wavelengths most often used in deep-sky astronomical imaging. In the matrix of spots, examine the left hand column. These are the on-axis spots. The black circle in each one represents the diameter of the Airy disk. If the majority of the rays fall within the circle representing the Airy disk, a star image viewed at high power will be limited almost entirely by diffraction, and is therefore said to be diffraction-limited. By this standard, all three SCT designs are diffraction-limited on the optical axis. In each case, the Schmidt corrector removes spherical aberration for green light. Because the index of refraction of the glass used in the corrector plate varies with wavelength, the Schmidt corrector allows a small amount of spherical aberration to remain in red and blue light. This aberration is called spherochromatism, that is, spherical aberration resulting from the color of the light. While the green rays converge to a near-perfect point, the red and blue spot patterns fill or slightly overfill the Airy disk. Numerically, the radius of the Airy disk is 7.2µm, (14.4µm diameter) while the root-mean-square radius of the spots at all three wavelengths is 5.3µm (10.6µm diameter). Because the human eye is considerably more sensitive to green light than it is to red or blue, images in the eyepiece appear nearly perfect even to a skilled observer. Spherochromatism depends on the amount of correction, or the refractive strength, of the Schmidt lens. To minimize spherochromatism, high-performance SCTs have traditionally been ƒ/10 or slower. When pushed to focal ratios faster than ƒ/10 (that is, when pushed to ƒ/8, ƒ/6, etc.) spherochromatism increases undesirably. Next, comparing the EdgeHD with the classic SCT and the "coma-free" SCT, you can see that off-axis images in the classic SCT images are strongly affected by coma. As expected, the images in the coma-free design do not show the characteristic comatic flare, but off-axis they do become quite enlarged. This is the result of field curvature. Figure 3 illustrates how field curvature affects off-axis images. In an imaging telescope, we expect on-axis and off-axis rays to focus on the flat surface of a CCD or digital SLR image sensor. But unfortunately, with field curvature, off-axis rays come to sharp focus on a curved surface. In a "coma-free" SCT, your off-axis star images are in focus ahead of the CCD. At the edge of a 40mm field, the "coma-free" telescope's stars have swelled to more than 100µm in diameter. Edge-of-field star images appear large, soft, and out of focus. Meanwhile, at the edge of its 40mm field, the EdgeHD's images have enlarged only slightly, to a root-mean-square radius of 10.5µm (21µm diameter). But because the green rays are concentrated strongly toward the center, and because every ray, including the faint "wings" of red light, lie inside a circle only 50µm in diameter, the images in the EdgeHD have proven to be quite acceptable in the very corners of the image captured by a full-frame digital SLR camera. Field curvature negatively impacts imaging when you want high-quality images across the entire field of view. Figures 4 and 5 clearly demonstrate the effects of field curvature in 8- and 14-inch telescopes. Note how the spot patterns change with off-axis distance and focus. A negative focus distance means closer to the telescope; a positive distance mean focusing outward. In the EdgeHD, the smallest spots all fall at the same focus position. If you focus on a star at the center of the field, stars across the entire field of view will be in focus. In comparison, the sharpest star images at the edge of the field in the "coma-free" telescope come to focus in front of the on-axis best focus. If you focus for the center of the image, star images become progressively enlarged at greater distances. The best you can do is focus at a compromise off-axis distance, and accept slightly out-of-focus stars both on-axis and at the edge of the field. Any optical designer with the requisite skills and optical ray-tracing software can, in theory, replicate and verify these results. The data show that eliminating coma alone is not enough to guarantee good images across the field of view. For high-performance imaging, an imaging telescope must be diffraction-limited on-axis and corrected for both coma and field curvature off-axis. That's what you get with the EdgeHD, at a very affordable price. Field Curvature Telescope with Field Curvature Flat-Field Telescope FIGURE 3. In an optical system with field curvature, objects are not sharply focused on a flat surface. Instead, off-axis rays focus behind or ahead of the focus point of the on-axis rays at the center of the field. As a result, the off-axis star images are enlarged by being slightly out of focus. 6 I The Celestron EdgeHD