With a new, clearer Nikon eyepiece and a wider field of view, the Unistellar eVscope 2 smart 'scope can now be used to take sharper astro-photos of the Moon as well as distant galaxies, nebulae and stars clusters. However, its biggest attraction is that it deals expertly with light pollution.

MTF is one of the best tools available to quantify the overall imaging performance of a system in terms of resolution and contrast. As a result, knowing the MTF curves of each imaging lens and camera sensor within a system allows a designer to make the appropriate selection when optimizing for a particular resolution.

A theoretical modulation transfer function (MTF) curve can be generated from the optical prescription of any lens. Although this can be helpful, it does not indicate the actual, real-world performance of the lens after accounting for manufacturing tolerances. Manufacturing tolerances always introduce some performance loss to the original optical design since factors such as geometry and coating deviate slightly from an ideal lens or lens system. For this reason, in our manufacturing sites, Edmund Optics® invests in optical test and measurement equipment for quantifying MTF. This MTF test and measurement equipment allow for the characterization of the actual performance of both designed lenses and commercial lenses (whose optical prescription is not available to the public). As a result, precise integration - previously limited to lenses with known prescriptions - can now include commercial lenses.

Yes, the eVscope is higher resolution than its forbear, but in part those extra pixels help to make up for its slightly wider field of view. So while the 7.7 megapixels are very welcome, you're not going to be wowed by ultra HD views.

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For an aberration-free image with a circular pupil, MTF is given by Equation 4, where MTF is a function of spatial resolution $\small{\left( \xi \right)}$, which refers to the smallest line-pair the system can resolve. The cut-off frequency $\small{\left( \xi _c \right)}$ is given by Equation 6.

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Modulation transfer function (MTF) is one of the most important parameters by which image quality is measured. Optical designers and engineers frequently refer to MTF data, especially in applications where success or failure is contingent on how accurately a particular object is imaged. To truly grasp MTF, it is necessary to first understand the ideas of resolution and contrast, as well as how an object's image is transferred from object to image plane. While initially daunting, understanding and eventually interpreting MTF data is a very powerful tool for any optical designer. With knowledge and experience, MTF can make selecting the appropriate lens a far easier endeavor - despite the multitude of offerings.

The Unistellar eVscope 2 digital telescope has a new eyepiece, a wider field of view and puts higher-res views of galaxies, nebulae and stars clusters on your phone or tablet. Here's our review

The eVscope is so easy to set up. Once it's mounted on its tripod (complete with spirit level to get it flat) using two thumbscrews, you download the app, switch-on the telescope, tune-in to its WiFi Direct network, remove the lens cap and eyepiece cover, and press a button on the app to have indulge in 'Autonomous Field Detection'. All that means is that it cross-references what stars it sees with some built-in planetarium software, as well as using your phone's GPS to work out where it is and what it should be seeing. It works more quickly if you use the arrow keys on the app to gently point it south/south-east where the Milky Way is … the more stars, the better! Obviously, you need a clear night.

Figure 6 plots the MTF of an aberration-free image with a rectangular pupil. As can be expected, the MTF decreases as the spatial resolution increases. It is important to note that these cases are idealized and that no actual system is completely aberration-free.

In imaging applications, the imaging lens, camera sensor, and illumination play key roles in determining the resulting image contrast. The lens contrast is typically defined in terms of the percentage of the object contrast that is reproduced. The sensor's ability to reproduce contrast is usually specified in terms of decibels (dB) in analog cameras and bits in digital cameras.

The Unistellar eVscope 2 is a digital telescope from the Maseille-based company. What exactly is a digital telescope? It's a regular telescope that's fully motorised and controlled exclusively via an app on a smartphone or tablet. However, as well as getting telescopes to slew to various deep sky targets just at the touch of a button, a digital telescope is fitted with a camera sensor, so in that way it's as much about astrophotography as amateur astronomy.

The eVscope seems, at first, to be identical to its predecessor. It has the same light grey tube and comes propped-up on a large tripod with three-section legs. Each is held steady by large, solid cams.

To properly define the modulation transfer function, it is necessary to first define two terms required to truly characterize image performance: resolution and contrast.

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Having created the first digital telescopes that use a camera sensor to deliver deep sky images to an app on a smartphone, Unistellar abandoned the idea of physically looking through a telescope with the launch of its eVscope eQuinox telescope in March 2021. However, not only does the eVscope 2, which launched in autumn 2021, see the return of an eyepiece, but it's made by no less a company than Nikon.

When this same principle is applied to the imaging example in Figure 1, the intensity pattern before and after imaging can be seen (Figure 4). Contrast or modulation can then be defined as how faithfully the minimum and maximum intensity values are transferred from object plane to image plane.

The ambient LED glow over every city on Earth is an absolute nightmare for amateur astronomers, but somehow the eVscope's filters and stacking tech helps get over it. Being able to image distant nebulae while not half a mile from a busy city centre is a thing of wonder. However, light pollution does make a difference. For example, during nights with a bright Moon it's best to point the eVscope at targets on the other side of the night sky, where it's much darker (after you're snapped the Moon, of course). It's also why the eVscope ships with that excellent backpack; so you can easily take it to truly dark rural skies. Do that and it can see objects down to a limiting magnitude of 18.

Available to buy now, following its launch in autumn 2021, the eVscope 2 costs €3,799 / £3,399 / $4,199, which is rather pricier than the debut product, the eVscope, which cost €2,999 / £2,599 / $2,999. Unistellar seems (wisely) to have scrapped its shipping charge, so there's free delivery in all major territories. There's a large tripod and a large, custom-made (and very comfortable) backpack included in the box.

A greater area under the MTF curve does not always indicate the optimal choice. A designer should decide based on the resolution of the application at hand. As previously discussed, an MTF graph plots the percentage of transferred contrast versus the frequency (cycles/mm) of the lines. A few things should be noted about the MTF curves offered by Edmund Optics®:

Resolution is an imaging system's ability to distinguish object detail. It is often expressed in terms of line-pairs per millimeter (where a line-pair is a sequence of one black line and one white line). This measure of line-pairs per millimeter $ \small{\left(\tfrac{\text{lp}}{\text{mm}}\right)} $ is also known as frequency. The inverse of the frequency yields the spacing in millimeters between two resolved lines. Bar targets with a series of equally spaced, alternating white and black bars (i.e. a 1951 USAF target or a Ronchi ruling) are ideal for testing system performance. For a more detailed explanation of test targets, view Choosing the Correct Test Target. For all imaging optics, when imaging such a pattern, perfect line edges become blurred to a degree (Figure 1). High-resolution images are those which exhibit a large amount of detail as a result of minimal blurring. Conversely, low-resolution images lack fine detail.

Knowledge Center/ Application Notes/ Optics Application Notes/ Introduction to Modulation Transfer Function

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What is new to the eVscope 2 is more contrasty images with deeper blacks and richer star fields. We're talking here about better images – delivered as good quality PNG files – that are great for viewing on phones and tablets, and for sharing online. You can zoom in on them within the app up to 400x, but it's best not to go that far.

That eyepiece has a lot to work with. Inside the eVscope 2 is an all-new Sony IMX347 CMOS image sensor, which is capable of 3200x3200 pixel images. That's 7.7 megapixels, which is something of a leap from the 4.8 megapixel images offered by the original eVscope and the eVscope eQuinox. Crucially, the eVscope 2 also has a new, wider field of view, so as well as getting views of distant galaxies and nebulae you can also now get a full screen view of the Moon and the stunning Andromeda Galaxy. However, planets don't look good … aside from Jupiter.

Now that the components of the modulation transfer function (MTF), resolution and contrast/modulation, are defined, consider MTF itself. The MTF of a lens, as the name implies, is a measurement of its ability to transfer contrast at a particular resolution from the object to the image. In other words, MTF is a way to incorporate resolution and contrast into a single specification. As line spacing decreases (i.e. the frequency increases) on the test target, it becomes increasingly difficult for the lens to efficiently transfer this decrease in contrast; as result, MTF decreases (Figure 6).

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It's one of a trio of improvements. With a new wider field of view and a higher resolution Sony sensor inside, the eVscope 2 is surely the most refined digital telescope yet. It's one of the best telescopes we've tried, and because it's so incredibly easy to use, it's also one of the best beginner telescopes (albeit one of the most expensive). Read on for our full Unistellar eVscope 2 digital telescope review.

With a new wider field of view and a few more pixels to play with, the eVscope 2 is a a souped-up smart scope that's great for polluted skies. This hugely likeable digital telescope serves as a great introduction – albeit a hugely expensive one – to the world of amateur astronomy and astrophotography, but without any of the hassle.

Once you're set up the app presents to you the choice of objects, from galaxies and nebulae to stars and the Moon, that are currently high above the horizon and ideal for observing. The app has a built-in catalogue of about 5400 objects to choose from.

A practical way of understanding line-pairs is to think of them as pixels on a camera sensor, where a single line-pair corresponds to two pixels (Figure 2). Two camera sensor pixels are needed for each line-pair of resolution: one pixel is dedicated to the red line and the other to the blank space between pixels. Using the aforementioned metaphor, image resolution of the camera can now be specified as equal to twice its pixel size.

Consider normalizing the intensity of a bar target by assigning a maximum value to the white bars and zero value to the black bars. Plotting these values results in a square wave, from which the notion of contrast can be more easily seen (Figure 3). Mathematically, contrast is calculated with Equation 3:

You can watch either through the eyepiece (though don't touch the telescope) or at your phone or a tablet as the object in question gets brighter and more defined with time. Some faint nebulae are worth observing for a long time, others look great after just a few seconds. Either way, you can download them to devices and share them instantly.

Correspondingly, object resolution is calculated using the camera resolution and the primary magnification (PMAG) of the imaging lens (Equations 1 – 2). It is important to note that these equations assume the imaging lens contributes no resolution loss.

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Under the same testing parameters, it is clear to see that #59-871 (with a better MTF curve) yields better imaging performance compared to #54-855 (Figures 11 – 12). In this real-world example with these particular 1951 USAF elements, a higher modulation value at higher spatial frequencies corresponds to a clearer image; however, this is not always the case. Some lenses are designed to be able to very accurately resolve lower spatial frequencies, and have a very low cut-off frequency (i.e. they cannot resolve higher spatial frequencies). Had the target been group -1, elements 5-6, the two lenses would have produced much more similar images given their modulation values at lower frequencies.

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The magic happens when you slew an object, which can take a while, though the eVscope is so accurate that we have no complaints. Once it has the object in its crosshairs you simply press the 'Enhanced Vision' button – a graphic of an eye – and it begins to take photos and stack them on top of each other. This is an advanced technique of astrophotographers and it helps produce incredible images even under light-polluted skies.

When optical designers attempt to compare the performance of optical systems, a commonly used measure is the modulation transfer function (MTF). MTF is used for components as simple as a spherical singlet lens to those as complex as a multi-element telecentric imaging lens assembly. In order to understand the significance of MTF, consider some general principles and practical examples for defining MTF including its components, importance, and characterization.

In traditional system integration (and less crucial applications), the system's performance is roughly estimated using the principle of the weakest link. The principle of the weakest link proposes that a system's resolution is solely limited by the component with the lowest resolution. Although this approach is very useful for quick estimations, it is actually flawed because every component within the system contributes error to the image, yielding poorer image quality than the weakest link alone.

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Conceptually, MTF can be difficult to grasp. Perhaps the easiest way to understand this notion of transferring contrast from object to image plane is by examining a real-world example. Figures 8 - 12 compare MTF curves and images for two 25mm fixed focal length imaging lenses: #54-855 Finite Conjugate Micro-Video Lens and #59-871 Compact Fixed Focal Length Lens. Figure 8 shows polychromatic diffraction MTF for these two lenses. Depending upon the testing conditions, both lenses can yield equivalent performance. In this particular example, both are trying to resolve group 2, elements 5 -6 (indicated by the red boxes in Figure 10) and group 3, elements 5 – 6 (indicated by the blue boxes in Figure 10) on a 1951 USAF resolution target (Figure 9). In terms of actual object size, group 2, elements 5 – 6 represent 6.35 – $ 7.13\tfrac{\text{lp}}{\text{mm}} $ (14.03 - 15.75μm) and group 3, elements 5 – 6 represent 12.70 – $ 14.25 \tfrac{\text{lp}}{\text{mm}} $ (7.02 - 7.87μm). For an easy way to calculate resolution given element and group numbers, use our 1951 USAF Resolution Edmund Optics Tech Tool.

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However, there are several changes. The new Nikon Electronic Eyepiece is very impressive. Branded with the camera-maker's logo, it's a lot clearer, more detailed, and much more involving than the eyepiece used on the original eVscope. Stars, nebulae and galaxies are presented against the jet black of space, and there's plenty of eye relief, which is good if you wear glasses. You can focus the eyepiece separately using a small knob.

There's a focus wheel on the underside of the eVscope. Although you can just manually focus on the Moon, it's best to use the Bahtinov mask. It's hidden in the lens cap. You put this plastic disc across the end of the telescope tube, point the eVscope at a bright star, then focus the telescope until you see three angled spikes of light. It's easy to do.

Every component within a system has an associated modulation transfer function (MTF) and, as a result, contributes to the overall MTF of the system. This includes the imaging lens, camera sensor, image capture boards, and video cables, for instance. The resulting MTF of the system is the product of all the MTF curves of its components (Figure 7). For instance, a 25mm fixed focal length lens and a 25mm double gauss lens can be compared by evaluating the resulting system performance of both lenses with a Sony monochrome camera. By analyzing the system MTF curve, it is straightforward to determine which combination will yield sufficient performance. In some metrology applications, for example, a certain amount of contrast is required for accurate image edge detection. If the minimum contrast needs to be 35% and the image resolution required is $ 30 \tfrac{\text{lp}}{\text{mm}} $, then the 25mm double gauss lens is the best choice.

To understand the relation between contrast and image quality, consider an imaging lens with the same resolution as the one in Figure 1 and Figure 4, but used to image an object with a greater line-pair frequency. Figure 5 illustrates that as the spatial frequency of the lines increases, the contrast of the image decreases. This effect is always present when working with imaging lenses of the same resolution. For the image to appear defined, black must be truly black and white truly white, with a minimal amount of grayscale between.