Pinholecamera

Red indicates poor matching.  At the top of the chart, your stars will be undersampled, resulting in a loss of resolution and square stars.  At the bottom of the chart, your star images will be large blobs; in other words, oversampling.  Oversampling results in an unnecessary loss in signal-to-noise ratio.

In conventional photography your lenses are highly adaptable, with adjustable f/ratio and often zoom capability (adjustable focal length).  On dedicated science instruments such as telescopes and microscopes you are much more limited by the optics, and you need to pick your camera to suit your optics. The key parameter is the physical size of the pixels, which may range from less than 1 micrometer (micron) across for a cell phone camera, to as much as 25 microns for large specialty scientific imagers.

Videocamera

Try: NIKKOR Z 70-180mm f/2.8, NIKKOR Z 85mm f/1.8 S, NIKKOR Z 135mm f/1.8 S Plena, NIKKOR Z 70-200mm f/2.8 S, NIKKOR Z DX 50-250mm f/4.5-6.3 VR

How large a spot this produces on the sensor depends on the focal length of the instrument, not the focal ratio. A handy formula is:

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A camera sensor is a silicon-based chip that records light data captured through the lens. Instead of using film to record an image, digital cameras use this ...

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If you had a simple lens made of a tube with one piece of optical glass at the front that focused the incoming light rays on a point at the back of the tube, the length of the tube would be the focal length of the lens. Modern lenses, however, use lots of different pieces of glass inside the casing to move light around before it hits the sensor and therefore focal length has nothing to do with the physical length of your lens. You can find two 85mm lenses that are completely different in size while, for example, the new NIKKOR Z 600mm f/6.3 VR S is less than 300mm in length.

For small telescopes, and in laboratory settings, the optics dominate. Assuming the optics are working to their full potential, the spot size is determined as follows:

Image

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You should also bear in mind that focal length translates differently on a DX camera (such as the Nikon Z 30, Z 50 or Z fc) compared to an FX ‘full-frame’ camera because the sensor on a DX camera is 1.5 times smaller than the FX sensor. For example, if you put a 50mm lens on a DX camera, you will actually get the angle of view and magnification similar to an 75mm lens on an FX camera (because 50 x 1.5 =75).

The first step is to determine your images scale in arc-seconds per pixel.  This table will help you do that.  Look up your telescope’s focal length on the left, and your camera’s pixel size along the top.  That will give you the image scale in arc-seconds per pixel.  (Or use the above formula.)

The focal length of a lens also affects the perspective of an image. With a long lens, perspective tends to be compressed, with objects in the background appearing closer to the subject in the foreground, whereas with a wide-angle lens the relative distance between two appears greater.

But there’s more. Depth of field determines what part of the image is in focus going from front to back. Lenses with longer focal length tend to have a shallower depth of field, meaning you can focus on and separate (or isolate) a particular object far away, whereas shorter lenses have a deeper depth of field, which means you can get more objects in focus throughout the image.

From 24mm to 35mm, lenses are wide angle. These are beloved by landscape, interiors and architecture photographers, as well as being useful for street scenes and dramatic pictures of the night sky. Get close to your subject and you will accentuate the perspective in the scene. A wide angle is a great travel companion, allowing you to shoot landscapes, cityscapes, people and much more.

Cameralens

Optooptics

What is immediately obvious is a larger telescope tends to have a longer focal length, and thus requires larger pixels.  Conversely small telescopes are better suited to small pixel cameras.  This is one reason why we offer a range of different camera models with different sensor characteristics.

The most important thing about focal length, however, is not what it is, but what it does. Focal length defines two main things about any lens: its magnification and its angle of view.

As angle of view goes down, magnification goes up. For example, a 24mm lens has a wide angle of view (around 84 degrees) and low magnification – perfect for sprawling landscapes. A 600mm lens has a very narrow angle of view and large magnification – great for taking close up shots of faraway wildlife (especially useful when you don’t want to get too close to a lion!).

You should also consider the field-of-view of your system. If you take the pixel size in arc-seconds and multiply by the number of pixels, that gives you the field of view the camera sees.

In order to perfectly replicate an image, you need to sample at least 2X the highest spatial frequency in the image. This Nyquist Sampling Criteria has been mathematically proven to record all the information present in the image. Unless you are doing profile-fitting photometry, where you need to measure the shape of the PSF accurately, it is usually sufficient to use 2 pixels across the FWHM of the star. In practice pixels are square and the star images are round, so 2.5 to 2.8 pixels is generally considered optimal. Increasing beyond this point does not increase the image detail; however, it does spread the light out and can reduce the signal-to-noise ratio. Spreading the same light among more pixels increases noise because each pixel has its own noise contribution.

From 35mm and 70mm, we have the ‘standard’ focal length, which is pretty close to what the human eye sees. Photographers talk about the ‘nifty fifty’ – a large aperture 50mm prime lens such as the NIKKOR Z 50mm f/1.8 S – because a 50mm lens is an ideal day-long companion, suitable for so many different types of shooting, especially in low light situations or indoors. This type of lens also creates a shallow depth of field and great bokeh blur.

SLRcamera

Astronomers have it easy because they have a universe of perfect point-spread functions all around them. Stars are so remote, compared to their diameter, that they appear as perfect pointlike sources. It is straightforward to evaluate the resolution performance of an astronomical telescope.  In a laboratory setting you may have to resort to specialized test equipment or work with theoretical numbers.

In practice, you want an absolute minimum of 2 pixels across the FWHM; 2.5 to 3 is an excellent match, and up to 4-5 will produce good results. It may be advantageous to lean towards a higher number, so that on those rare nights of excellent seeing you can take full advantage of the conditions.

Shuttercamera

Check out these images of the same scene shot from the same position but with focal lengths from wide angle 24mm to telephoto 180mm and you can see how the angle of view gets narrower as the magnification gets larger.

Browniecamera

Usually between 70mm and 200mm, a telephoto lens is a popular choice for portraiture and weddings (especially an 85mm focal length) and at the longer end is great for wildlife where you can’t get too close to the subject. At the longer end, a telephoto lens gives you the freedom to shoot as an observer where the subject is unaware of the camera, and so is also great for fly-on-the-wall, reportage-style shooting. This is also the focal length range for many macro lenses.

Camera lenses are usually described by two main factors: one is the aperture or f-number (the maximum size of the hole where light gets through to the sensor, where the lower the number, the bigger the hole). The other is focal length, which is in millimetres. You will usually see lenses described by focal length first and then aperture, for example 85mm f/1.8.

Lens choice can often be difficult, especially with so many options in the Nikon Z mount range (and access to another 300 or so Nikon F mount lenses with the FTZ II converter). So, here’s a quick guide to the different focal lengths and what they often get used for to help you.

Now we can determine how that matches with your observing conditions.  Across the top of the second chart is your FWHM seeing disk.  The range of “Excellent” to “Fair” represents typical seeing that we have in the Ottawa, ON region where our office is located.  Your local conditions may be better or worse than this. The chart gives you the number of pixels across the FWHM of a star image.  Remember, for good resolution imaging we need at least 2 and preferably 2.5 to 2.8, but no more than about 5 pixels across the FWHM.

At a typical green wavelength of 0.550 microns, an f/5 system will produce a spot 3.4 microns in diameter. Clearly this requires a small pixel to sample adequately.

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When atmospheric seeing is taken into account, the spot size is often much larger. If you are at a premier observing site, such as the summit of Mauna Kea, the long-exposure seeing disk can be less than 1 arc-second. At most non-alpine locations seeing disks of 2 arc-seconds are only seen on the most exceptional nights. Such a site will typically have seeing on the order of 2.5 to 3.5 arc-seconds, depending on the weather conditions.

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Try: NIKKOR Z 20mm f/1.8 S, NIKKOR Z 14-30mm f/4 S, NIKKOR Z 17-28mm f/2.8, NIKKOR Z DX 12-28mm f/3.5-5.6 PZ VR, NIKKOR Z 24mm f/1.8 S

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Angle of view is how much of the scene your lens will capture from side to side (holding the camera horizontally). A wide angle of view takes in a lot, a narrow angle of view less. Magnification is how ‘close’ you get to the subject of an image with the lens, like a telescope.

Camera lenses are usually described by two main factors: one is the aperture or f-number (the maximum size of the hole where light gets through to the sensor, where the lower the number, the bigger the hole). The other is focal length, which is in millimetres. You will usually see lenses described by focal length first and then aperture, for example 85mm f/1.8.

Astronomers have a difficulty, though, which is called “seeing”. The atmosphere is comprised of cells of warmer and cooler air, which are constantly circulating due to convection. Warm air rises; cool air falls. Since cool air is denser it also has a higher refractive index. The atmospheric bubbling of warm and cool cells affects the path of light through the atmosphere in a random fashion, causing starlight to wander rapidly. For very small optics this just makes the star images wander about; for larger optics you will get multiple cells within the light path, resulting in the star image breaking up and moving in multiple directions at once. Tip/tilt guiders such as the SBIG AO-X can improve resolution by removing seeing-related image wander; large telescopes (above 1 meter diameter) can use advanced adaptive optics systems with wavefront sensors and “rubber mirrors” to tighten the images.

One other thing to consider:  in some cases you may want to deliberately violate these “rules”, if resolution is not your primary concern.  If you need to cover a large area it may be sensible to deliberately undersample.  Doing this makes the camera more sensitive to distributed sources such as nebulae.  It should be noted that once a star is reduced below the size of a single pixel, it is not going to become any brighter by shrinking it further.  Undersampling will emphasize distributed detail in comparison to star images.  The concept of “fast” f/ratios producing brighter images only applies to distributed sources.

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In order to get the best results from your equipment, it is important to match the resolution of your camera to the resolution of your optics.

Try: NIKKOR Z DX 24mm f/1.7, NIKKOR Z 26mm f/2.8, NIKKOR Z 28mm f/2.8, NIKKOR Z DX 16-50mm f/3.5-6.3 VR, NIKKOR Z 35mm f/1.8 S

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At 300mm and upwards, we have the super-telephoto range. This is most commonly used by sports and wildlife photographers, where it would be impossible to get close to the subject. At this range, and with such a narrow angle of view, it’s usually advisable to use a monopod or tripod to reduce camera movement (although Nikon’s in-camera vibration reduction (VR) and VR lenses can help with that), and also because lenses this size can be heavy to hold for long periods. Telephoto lenses can also be used with a teleconverter, which can double the focal length of the lens, giving you even more ‘reach’.

There are a variety of ways to characterize the resolution capability of optics. One of the most straightforward is to determine its response to a perfect point source – the resulting image of a perfect point is called a “point-spread function” or PSF.  In general, larger diameter optics provide more resolution, while shorter f/ratio optics produce smaller spot size.

Try: NIKKOR Z 180-600mm f/5.6-6.3 VR, NIKKOR Z 100-400mm f/4.5-5.6 VR S, NIKKOR Z 400mm f/4.5 VR S, NIKKOR Z 600mm f/6.3 VR S

If you had a simple lens made of a tube with one piece of optical glass at the front that focused the incoming light rays on a point at the back of the tube, the length of the tube would be the focal length of the lens. Modern lenses, however, use lots of different pieces of glass inside the casing to move light around before it hits the sensor and therefore focal length has nothing to do with the physical length of your lens. You can find two 85mm lenses that are completely different in size while, for example, the new NIKKOR Z 600mm f/6.3 VR S is less than 300mm in length.

Any lens with a focal length of between 8mm and 24mm is usually described as an ultra-wide. You’ll be taking in a huge angle of view of what’s in front of the camera. These are lenses for getting in really close with your subject to create drama and are also used extensively for astrophotography. However, at really low focal lengths there will be significant distortion at the sides of the image where straight lines start to look curved. Ultra-wides are one the hardest lenses to master but, with effort, they can deliver incredible results.

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There are two types of lenses: primes, which have a fixed focal length, and zooms, where the focal length is variable. Zooms are super-handy as you often only have to carry one lens around that will be capable of shooting lots of different subjects, from landscapes to portraits, so it’s great for travel. Prime lenses, however, are usually lighter and are often available with larger apertures than zooms.

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A camera with 9 micron pixels attached to a telescope with a 2000 mm focal length will result in 0.9 arc-seconds per pixel.