6
I
The Celestron EdgeHD
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.
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.
Telescope with Field Curvature
Field Curvature
Flat-Field Telescope
