Welcome to Houston Astronomical Society

By Don Selle

Part 1 of Getting You Exposed, dealt with the concept of Total Exposure time and Exposure Value. It also provided some rules of thumb to help you estimate the Total Exposure time required for various types of targets using your own imaging rig. Having a good idea of the Total Exposure is certainly essential for acquiring high quality data on the low light level targets we image, but it is only one factor we need to consider.

Since most targets will require several hours of Total Exposure time to acquire enough data to assemble a quality image, we will typically acquire that data using multiple sub-exposures (aka sub-frames). The exposure time for each sub-frame when summed will equal the Total Exposure time of the acquired data.

When you think about it, this makes sense. You wouldn’t want to take hours long single exposures as too much can happen. Satellite photo-bombs, mount tracking errors, autoguiding errors, operator error and things that bump your tripod in the night can ruin your sub-frames and result in the waste of a lot of time. Even back in the days of film, to avoid these risks, astro-imagers took multiple exposures, developed them, then scanned and electronically combined them to reduce the noise in the image.

Once the decision is made to make up the Total Exposure time through some number of shorter duration sub-frames, the question arises – how long should each sub-exposure be? Since the risk to individual subframes increases as sub-frame exposure time, shorter may be better, but how to know.

Back in the day when I got started astro-imaging, there was no set answer.  The best advice at the time was to set your sub-frame exposure long enough so that the “hump” in the sub-frame histogram started at 25%-33% of the left side of the graph.

I didn’t know it at the time, but this rule of thumb was a statement of the photographic technique commonly referred to as “exposing to the right” or increasing the exposure of your photograph so that details in the shadows are sufficiently exposed but the highlights are not saturated or “blown out”. This way, the darker details can be recovered during processing.

A little explanation is in order here. The photo on the left is a crop from a single sub-frame (it is raw i.e., no processing) with a histogram of the complete frame shown on top of it. The histogram shows the range of pixel brightness levels (0-255-actual values converted to 8-bit color) from left to right across the bottom of the graph with the total number of pixels in the frame which are at each of the brightness levels. While it is not totally apparent, each of the three RGB color channels is displayed on the histogram, as well as statistics for the whole image at the bottom. (There is a lot more information in the histogram, but that’s the subject of a future article!).

This histogram pretty well illustrates the expose to the right rule of thumb. In truth, I estimated the exposure time based on a method which I will describe for you. It relies heavily on the mathematical theory behind signal processing and has been reduced to a couple of simplified calculations and software tools. When the appropriate values representing the performance of your imaging system and the quality of the night sky you are under, will provide a very good estimate of the optimum sub-frame exposure time.

When I updated my imaging system, replacing my older mono CCD camera with a new OSC CMOS camera, I initially continued to use the same routine sub-frame exposure times. I later learned (from my friend and advanced imager John Talbot 1) about how improvements in camera technology which have been incorporated into the newer CMOS cameras can help improve the raw data you capture. I recently have begun to use a new method of estimating my sub-frame exposure times which is based on mathematical signal processing theory as applied to imaging.

I will not go too deeply into the theory. For those who are mathematically inclined and interested should spend an hour and watch Dr. Robin Glover 2, the developer of SharpCap describe the theory and how it is used. Dr. Glover has extended the work done by others and developed some very interesting tools which he has included in SharpCap which will do the calculations for you. In truth, once you have the right information about your camera, optics and the sky brightness where you image, thanks to calculator Glover has made available on the SharpCap website, you can make a very good estimate of optimum sub-exposure time with a simple hand calculation. A precise calculation requires that you take an image of the night sky so that the sky brightness can be measured.

It is worth noting that Glover is neither the first nor the only person to develop the theory and tools necessary to determine optimum sub-frame exposure time using signal theory, and Glover’s approach is very similar to and compatible with what has been done previously which required a direct measurement of sky brightness.

In the current era of very low noise CMOS cameras, Glover has championed the idea of taking very many short exposure sub-frames which in some applications, might eliminate the need for autoguiding, and allow use of mounts with less precise tracking. Dr. Glover has also provided an online tool to assist in estimating the sky’s brightness in order to estimate the optimum sub-frame exposure time.

Signal Processing Theory

Determination of the optimum sub-frame exposure time is based on the application of signal processing theory applied to astro-images. All of the sources of noise that end up in each sub-frame are identified and quantified. These noise sources can be organized into two categories, systematic noise and shot noise.

Systematic Noise - is noise such as dark current or thermal noise and bias pattern noise. This noise can be directly removed from the subframes during calibration with only a small random amount remaining.  (See my AP Corner “Let’s Get You Calibrated” https://www.astronomyhouston.org/newsletters/guidestar/ap-corner-let%E2%80%99s-get-you-calibrated#overlay-context=welcome

Shot Noise – Removing systematic noise leaves what is commonly termed Shot Noise, or the noise which is specific to each sub-exposure. Shot noise is comingled in the raw frame and is not removed during image calibration and consists of two major noise sources – Sky Noise and Read Noise. Shot noise is dealt with during image processing, after the calibrated sub-frames are stacked to improve the Signal to Noise Ratio.

Sky Noise This is primarily noise coming from the sky (a.k.a. Sky Background) which is not associated with either the stars or the target in your sub-frames. The biggest component of sky noise is light pollution, but even at the darkest sites there is still a sky background. It is made up of the dim diffuse natural light reaching the Earth from space, as well as the natural sky glow which is due to the light given off by ions created by sunlight striking the atmosphere, when they recombine. Sky noise is mostly removed by subtraction with a small random fraction remaining.

Read Noise Noise is added to each sub-frame by the camera and is commonly called Read Noise. It is generated during the process of collecting the photons, converting them to electrons and then reading them out and converting them from a voltage into a digital number. Read noise (along with any random sky noise) is dealt with by noise reduction algorithms during image processing.

Optimum Sub-frame Exposure - We do need to define what optimum means. The assumption is that as we described above, the risk of outside factors messing up a sub-frame increase with increasing exposure time. This means that finding the shortest exposure which can sufficiently capture the faint detail present in our targets and capturing enough of them in order to significantly improve the signal to noise ratio of these faint details is the optimum sub-exposure time.

Determining Optimum Sub-Frame Exposure Time

The most accurate way to determine your sub-frame exposure is to use a tool which actually makes measurements of your camera and of the sky glow at your imaging site. SharpCap3 has a comprehensive tool to do this for supported cameras called Smart Histogram. When coupled with the Sensor Analysis Tool SharpCap will take images of the night sky, determine the key parameters for your system and measure the sky noise, then do a full calculation for you, of how long your sub-frames should be exposed, and how many to take. I’ve personally not used it but I have gotten good reports from several imagers who have. Frankly, the tools sound very impressive, especially if you use SharpCap and are willing to spend the time measuring the sky background.

If you are like me and already have invested considerable time into learning and setting up an imaging software system and would prefer not to switch horses. You can easily calculate a good estimate of optimum exposure time with the following equation:

R = Camera Read Noise (RN) in electrons

P = Sky Noise rate measured by your camera in electrons per second

C = Preferred % Read noise is of total Shot Noise (where Shot Noise = Read Noise + Sky Noise)

% RN     C Factor

1%         = 50

2%         = 25

5%         = 10

10%       =  5

20%       =  2.3

25%       =  1.8

 

The calculation I made for the example sub-frame exposure was as follows:

R = 2.2 electrons at ISO 3200 for my Canon 6D and a 300mm f/4L lens - value based on review on www.ClarkVision.com

P = 1.92 electrons per sec for Bortle 4.0 location

C = 50

Recommended exposure = 126 seconds – and I used 120 secs, a round number and because I was using a camera tracker and had verified that I was able to get reasonable results with 2-minute exposures without guiding.

Determining the R and C Factor Electrons

From the above formula it is clear that we need to determine two key factors, the read noise in terms of electrons, and the sky background rate in terms of electrons generated in each pixel per second due to the sky flux. Fortunately, there are good resources to determine both values.

Camera Read Noise Electrons

If you own a recent model astro-imaging camera you are in luck, as most manufacturers are now specifying the read noise inherent in their cameras in terms of electrons. Some are even providing data fully characterizing the camera performance at various levels of gain, as shown below for a very popular ZWO monochrome camera. In addition, SharpCap also contains a tool that will allow you to test your own camera.

For DSLRs though, the situation is a little more complicated in that the manufactures such as Sony Canon and Nikon do not publish this information. Fortunately there are several good sources where talented individuals have made the effort to test and publish data on popular DSLRs. For older model DSLRs, especially by Canon, and some Nikons models you can find data on many models on the ClarkVision.com website at:

https://clarkvision.com/articles/digital.sensor.performance.summary/index.html

For a more comprehensive set of data for many DSLR manufacturers and models you can check out the website photonstophotos.net which has a comprehensive set of read noise data.

https://www.photonstophotos.net/Charts/RN_ADU.htm

If your camera is in both sources, my preference would be to follow ClarkVision since its author Roger Clark is focused almost entirely on nightscapes and astrophotography.

Sky Noise Electrons

The calculation to determine sky background is based on the site you are imaging from, the optics you are using, including any filters and characteristics of your camera. Fortunately for us, Dr. Robin Glover has provided a very straightforward website tool that makes this calculation very easy.

http://www.tools.sharpcap.co.uk/

 

My friend John Talbot has even suggested setting up a spreadsheet to help you plan for imaging with various imaging rigs and at various sites. Keep in mind that the results of this calculation are just very good estimates, so use them accordingly as suggestions. If you want to make the estimation even more accurate without imagining, you might even use a Sky Quality Meter (SQM) to measure your sky brightness!

Clear skies and happy imaging!

Notes

1. Equations and spreadsheet example come from a talk my friend John Talbot gave at both the 2022 Advanced Imaging Conference and at the 2022 Okie-Tex Star Party. You can see a video of John’s AIC talk here: https://www.advancedimagingconference.com/articles/new-generation-cmos-technology-jon-talbot

You will need to join the AIC website; it is free and the full library of videos from past conferences is available for viewing. Join AIC here: https://www.advancedimagingconference.com/subscribe

 

2. Dr. Glover’s video https://www.youtube.com/watch?v=3RH93UvP358
3. https://www.sharpcap.co.uk/sharpcap/features/smart-histogram

by Jim King

Learn the basics, then work on getting better and having more fun

BARLOW LENS: This type of lens which you install in your telescope’s focuser (and then put an eyepiece into) increases the effective focal length of a telescope and magnifies its image.  A 2x Barlow doubles the focal length and the eyepiece will provide twice the power.  If you choose the eyepieces carefully, adding a Barlow can give you a much wider range of magnifications.  

BINOCULARS: High-quality binoculars should be part of every observer’s kit.  For magnification, choose 7x, 8x or 10x.  The front lenses should be at least 50 mm across.  Smaller ones don’t collect enough light.  If your budget can stand it, check into Image Stabilized (Canon, Fuginon) binoculars to avoid having to rely on the availability of a tripod.  I have the Canon 10X30s image stabilized which are a true “grab and go” accessory for astronomy, bird-watching, etc.

CIRCUMPOLAR STAR: This term describes a star that always lies above an observer’s day or season. At the equator, no star is circumpolar.  At the North or South Pole, all stars are circumpolar.  At any other latitude, a star whose declination is greater than 90 degrees minus the observer’s latitude will be circumpolar.

COLLIMATION: Owners of Newtonian or Schmidt-Cassegrain telescopes who don’t have them set up in a permanent location, should collimate their scope, or align its components, prior to each observing session.  See the telescope’s operation manual or You Tube to learn the procedure.  (I have three Schmidt-Cassegrain telescopes, none of which have ever required collimation as long as proper handling and care are exercised...properly cased, not dropped or seriously bumped).

DARK ADAPTATION: In the first 30 minutes in a dark setting, the sensitivity of our vision increases 10,000-fold, with little gain after that.  Even brief exposure to bright light temporarily reverses the gain, though how much you lose depends on how long the light is on and its intensity.  Always opt to use dim red light or similar although even red lights can temporarily lessen eye acuity.

EYE PATCH: Cover your observing eye with a patch when you start to set up, and by the time you finish, you’ll have a fully dark-adapted eye.  Then, switch the patch to your other eye so you can keep both eyes open at the eyepiece, a technique that reduces eye fatigue.  Oh, and before you use your faint red light, move the patch back to your observing eye.  Interestingly, the pirates of old wore eyepatches, not because they lost an eye, but to help them see better at night.  True story. 

FOCUS: Here’s the most important tip on the list.  Each time you put your eye to your eyepiece, and whenever you change eyepieces, refocus.  If you do not, you are wasting valuable observing time.

HORIZON: We usually define the horizon as where the celestial sphere intersects Earth at every point. Here’s the problem, most non-ocean locations don’t offer a true horizon…that is, one 90 degrees from the zenith.  Mountains, hills, buildings, trees can all obstruct your view.  Be aware that the times celestial objects rise and set will be affected by your local horizon.

INTOXICATION: Ever notice that all observing guides recommend you bring nonalcoholic beverages when you observe? The reason is simple, alcohol impairs vision.

KNOW YOUR EQUIPMENT: You just bought a new telescope.  Don’t rush to take it to a remote site.  Set it up at home first, and in the daytime.  Just be careful NOT to point it at the Sun.  Any problem you uncover in the daytime, will be one issue less you’ll have to deal with in the dark.  And if you come across an issue, at least you’ll be familiar with the scope.  The Moon is frequently available to us in broad daylight.

LIMITING MAGNITUDE: The best way to get a feel for the quality of your observing site is by measuring its limiting magnitude (L.M.).  Most observers determine LM by identifying the faintest star they can see at the zenith.  Other like to use the region around Polaris because the same stars are visible year-round.  Your telescope operating manual can give a fair approximation of the telescope’s designed L.M.

MERIDIAN: An observer should always know the position of the meridian. It’s the great circle that passes through the zenith and the celestial poles.  Find, Polaris, draw a line to the zenith, and continue south.  When an object lies on the meridian, it has reached its highest point and is best place for observing.

NEW GENERAL CATALOGUE (NGC): Most observers are familiar with at least the main Messier objects.  The NGC is a more extensive catalogue of deep-sky objects.  The original catalogue (established in the year 1888) listed 7,840 objects, with 5,386 more added later.  Get familiar with the designations, and positions of some of the most impressive NGC objects to expand your repertoire.  A few of the brighter ones to consider are NGC 457 (The Owl Cluster), NGC 869 and NGC 884 (The Double Cluster), NGC 5139 (Omega Centauri), and NGC 7293 (the Helix Nebula).

OBSERVING CHAIRS AND LADDERS: When observing, comfort is everything, and nothing says comfort like a high-quality observing chair.  Good ones have sturdy construction and padded seats and are easily adjustable.  While chairs work fine for refractors and Schmidt-Cassegrain’s, large Dobsonian-mounted scopes require a ladder.  In this case, look for ladders with wide, rubber-covered steps and a utility tray.  

POSITION ANGLE: Learn where north is when you look in your eyepiece.  Many times, observing guides will give the position angle (P.A.) of one object in relation to another, brighter object.  This angle is measured from north through east.  For a double star, it’s the line joining the primary with the companion star.

SEEING AND TRANSPARENCY: Seeing is a measure of the steadiness of the air.  Transparency is a measure of how clear the sky is.  Weather has a huge impact on both. An air mass colder than the ground will produce unsteady air, but it’s also usually dust-free.  An air mass warmer than the ground can hold lots of dust, but images will be a lot steadier.  If a cold front has just passed your site, the seeing probably won’t be good for at least 24 hours.  Seeing can be good if thin cirrus clouds are above you, except when they combined with low-level crosswinds.

SITE SELECTION: When you are looking for an ideal observing site, three things count.  First, it must be free of most light pollution. Second, the air must contain few aerosols (dust, air pollution, and water droplets), And third, it should be at an altitude between 5,000 and 8,000 feet.  Of course, perfection is illusive, but close can be good.

YOUR SPEED: Some observers spend an hour or more on a single object, endeavoring to glean every bit of detail possible.  Others take a more leisurely pace between 5 and 15 objects per hour.  Take the time to discover what observing speed works best for you and plan accordingly.  Great nights are few and far-between. 

ZOOM EYEPIECES: If your budget for observing accessories is limited, consider a zoom eyepiece.  Such an accessory will provide a range of magnifications at a cost much less than each of the individual eyepieces in its range combined.  Fortunately, the quality of today’s zoom eyepieces is much better than those of even a decade ago.

Source: Adapted from Astronomy Magazine, September 2022

Ex astris scientia, y’all

 

 

by Will Sager

If you own a telescope, you probably looked first at a refractor (Figure 1). It is the quintessential telescope and if you see a telescope in a cartoon, it is probably one of these. This is first telescope invented, often attributed to Galileo Galilei in 1609 although opticians in the Netherlands probably made similar instruments a few years before. But Galileo pointed his telescope skyward, extensively documenting his observations, and became the first telescopic astronomer. Galileo’s telescope used an objective lens to focus light on an eyepiece lens, which is the basic description of this type of scope. There are many different refractor telescopes, so a beginner can get confused without some background.  The goal here is to provide the reader with some details to help understand refractor telescopes and their designs.

 

Figure 1. A refractor telescope (aka “yard cannon”). (source: Opticalmechanics.com)

By the Numbers

Any telescope description comes with a bunch of numbers, so let’s first consider some important numbers that tell you about a refractor and its capabilities. Some important numbers are aperture, focal length of the objective, f-ratio, and eyepiece focal length (Figure 2). 

 

Figure 2. Simplified diagram of a refractor telescope. Dashed lines represent light rays entering the edges of the objective lens. (author figure)

 

The aperture is the width of the objective lens, which determines how much light the scope can capture and guide into your eyeball. Bigger is better. The amount of light collected depends on the objective area, which is pr², where r is the lens radius. If you double the diameter, say from 2 inches to 4 inches, you increase the light gathered by a factor of 4. The focal length is the distance between the center of the objective and the point at which the light going through the lens comes into focus. Focal length is important for two different properties: f-ratio and magnification. The f-ratio is the focal length divided by the aperture and it is a measure of image brightness. This is the same number that you find on your camera lens, where f-ratios <2 are considered “fast”. In photography, fast means that the brighter image requires a shorter exposure to capture an image. Common refractor telescope f-ratios are about f-7 to f-15. A 102 mm (4 inch) aperture with a focal length of 714 mm (28.1 inches) has an f-ratio of 7. At f-15, the focal length is 1530 mm (60 inches). That is a long scope. Why not have lower f-ratios? Because very fast lenses are difficult to make so that the image is sharp across the whole lens (i.e., expensive). Moreover, if the f-ratio is very low, not all of the light will go in your eye (see below). What is the benefit of a “slow” refractor with a high f-ratio? It is easier to make a lens that is sharp across the field. Another benefit is magnification.

 

Magnification is determined by the focal length of the primary lens divided by the focal length of the eyepiece. Eyepieces come in many focal lengths, but most are between about 30 mm (1.2 inches) for low power and 5 mm (0.2 inches) for high power. For example, our 714 mm focal length refractor yields 24x (this means the image is magnified by a factor of 24) for the 30 mm eyepiece (714/30 = 23.8) and 143x (714/5 = 142.8) for the 5 mm eyepiece. The former is good for low power sweeping across the Milky Way and the latter will give decent views of craters on the Moon, but the power is not very high for discerning details, for example, on planets. Thus, many planetary scopes have longer focal lengths. By comparison, the 1530 mm f-15 scope produces 51x and 306x for the 30 mm and 5 mm eyepieces, respectively. This seems great, but there is a catch. Telescopes will give a maximum useful magnification of about 50x times the aperture in inches. Above that magnification, the image becomes dimmer and fuzzier, but no additional detail can be discerned. Thus, your 102 mm aperture refractor can get up to 205x before it is maxed out. You need a bigger objective to go higher. (But don’t despair – high power is overrated and most of your viewing will be done at low power)

 

As mentioned above, refractors that have very low f-ratios won’t put all of the light in your eyeball. Why not? The answer is exit pupil diameter. The exit pupil diameter is the width of the light column coming out of the eyepiece into your eyeball. When fully dilated (night adapted) in the dark, most people have pupil diameters of about 7 mm. As people age, this maximum dilation is a bit less. If the exit pupil is larger than the diameter of your pupil, the light around the edges does not go in your eye (i.e., it is wasted). To calculate the exit pupil diameter, divide the aperture by the magnification. For example, 7x binoculars never have objective lenses >50 mm because 50/7 is 7.1. Any bigger objectives and the exit pupil is too large. Considering the 102 mm refractor once again, the 30 mm eyepiece at 24x produces an exit pupil of 4.3 mm. No problem. What if that scope were much faster, say f-4? Then the focal length would be 408 mm and the 30 mm eyepiece would yield only 13.6x and the exit pupil would be 7.5 mm. Whoops, too wide for your eyeball. Such a lens would be great for photography because it is fast and astro cameras don’t have narrow pupils. 

 

Another consideration for high f-ratio refractors is scope length. Remember that the 102 mm aperture f-15 scope has a length of 60 inches. This is the proverbial “yard cannon” that may cause your neighbors to call the police when you bring it out. Refractors are usually mounted by a clamp around the middle. This means that the focuser with the eyepiece sticks out about 30 inches from the mount attachment point. When you turn the focus knob, vibrations are magnified by this lever arm, which makes it difficult to see when the image is in focus. Poorly mounted long refractors can jiggle for many seconds after being touched. As a result, long refractors require heavy, sturdy mounts. 

 

An advantage for refractor telescopes is that they have rigidly mounted lenses, so that once collimated (i.e., the lens axes are aligned) – usually during manufacture – they tend to stay collimated. In contrast, most telescopes with mirrors require periodic adjustment to collimate the optical axes. This makes refractors good for travel scopes and for astronomers who don’t like to collimate. 

 

Before moving on, note one particular feature of the refractor diagram (Figure1). The light beam coming in on one side of the lens ends up coming out of the other side of the eyepiece. This geometry means that refractor images are upside down and backwards. If you use your scope to look at something terrestrial, this flip will be immediately obvious. When viewing the sky, it is mainly an inconvenience of which the observer should be aware. Binoculars, which are designed to give right-side-up images, have special prisms that turn the image around. For an astronomical telescope, the extra reflections cause slight image dimming, so the erecting prism is usually left out (but you can purchase one if you want).

 

Achromat and Apochromat, What’s the Diff?

Looking at refractor telescope ads, you will find a huge price range for scopes of similar size. Using the 4 inch refractor for example, Celestron sells a 102 mm refractor OTA (optical tube assembly, i.e., the tube without a mount) for about $300. In contrast, Tele Vue sells a 101 mm OTA for about $4,270. Why the big difference? The Celestron scope is an f-10 with an achromat lens whereas the Tele Vue is a fast f-5.5 with a Petzval lens. The Petzval lens is much more complicated and designed to create fast, sharp images for photography. Mostly the price difference reflects how well the lens focuses the image. Making a lens that produces pinpoint stars across the field of view is difficult.

 

All lenses suffer from aberrations. Chromatic aberration occurs because a single lens does not focus all wavelengths of light at the same distance from the objective (Figure 3). This divergence occurs because the lens behaves like a prism. This means that a simple lens can only be designed to make a sharp image for some wavelengths. Other wavelengths will appear as out-of-focus halos. Cheap refractors with poorly corrected lenses will show such fringes on bright objects and straight edges. A remedy for chromatic aberration is to put two lenses together with different refractive indices so that the second lens bends the divergent wavelengths more closely into focus. A common inexpensive approach is a two-lens objective (doublet) using one element of crown glass and one element of flint glass. The two glass types have different elements added that change the refractive index. This two-lens design is called an achromat. This is the type of lens used in most inexpensive refractors (Figure 4).

Figure 3. Diagram illustrating chromatic aberration, caused by the glass lens having different indices of refraction for different light wavelengths. The result is that different light wavelengths have different focal distances. (source: Bob Mellish, Wikipedia)

 

Figure 4. Diagram of a doublet achromat objective lens pair, showing reduced chromatic aberration. (source: Bob Mellish, Wikipedia)

 

An apochromatic objective (aka “apo”) is one that is designed for better color correction. Such telescopes often have a three-element lens (a triplet, Figure 5), but there are some doublets made with exotic (expensive) glass elements that provide decent correction for chromatic aberration. Doublet apos are often called semi-apochromatic. One can purchase a 4-element objective, called a Petzval, which contains two doublets. More lenses and more expensive glasses give better correction, but the more lenses and more expensive glasses make these objectives expensive to manufacture. This is why high-quality apo refractors have big prices.

 

Figure 5. Diagram of three-element apochromat objective lens assembly, which further reduces chromatic aberration. (souce: Egmason, Wikipedia)

 

Multiple-element objectives also help correct other aberrations. Any telescope objective produces spherical aberration, which is caused by the fact that light rays coming through the lens at different distances from the center are not guided to the same focus point (Figure 6). Coma is another imperfection, caused by off axis light rays not focusing at the same point (Figure 7). Well-designed multiple-lens objectives do a better job at correcting these aberrations and that is why they are more desirable, especially for photography, where sharp, pinpoint stars are desirable.

 

Figure 6. Diagram illustrating spherical aberration, caused by a lens not bringing all light rays (blue lines) to focus at a single point. (source: Mansurov, 2019)

 

Figure 7. Diagram illustrating coma, which is caused by off-axis light rays not converging to a single focus point. (source: Edmondoptics.com)

 

Which Refractor Scope for Me?

If you want a refractor, which scope is the right one for you? It depends on what you want to do with it. If you will primarily use the scope for visual observations, a good achromat will probably be just fine. It should probably have a higher f-ratio (around f-10) so that the aberrations are less and the longer focal length will allow you to get up to the maximum effective magnification. You might get some color fringes on bright objects, but the cost will be affordable. If the fringes bother you, consider getting a semi-apo doublet. It will be more expensive, but will be more pleasing to your discerning eye. If you want get into astrophotography, you probably want an three or four element apo with excellent color correction. 

 

As you scan telescope ads, you find that size and cost go hand-in-hand. You want a larger objective to collect more light and allow more magnification. Common consumer refractors max out at about 6-inches objective diameter. You can get a decent 6-inch Celestron achromat OTA for about $1,000. Apo refractor OTA will be a factor of 4-8 times more expensive. Larger refractor scopes are too expensive to manufacture at prices that many people will pay and larger objectives also translate it large, long tubes that require sturdy mounts, often a pier fixed in an observatory. As a result, one rarely encounters a refractor with a larger objective unless you visit a professional observatory. 

 

Reference:

Mansurov, N., 2019. What is spherical aberration? Photoraphylife.com

 

Lens design primer: https://www.pencilofrays.com/lens-design-forms/

by Loyd Overcash

Exposure was 135 minutes taken in 5 minute subs with my 14.5 RC and the ZWO-2600mc camera in Bin 3 Gain 300