Librescope: Reading Glasses That Eliminate Eye Strain

I pain, you pain, we all pain from eye strain. In this day of omnipresent screens and books, it's easy to finish a study session or workday feeling like your eyes will never relax again. Thankfully, there's a simple solution: this Instructable will guide you through how to make a Librescope ("libre," stemming from the Latin root for "book," and "scope" because these glasses work similar to a traditional telescope), which optically projects the image of the book you're reading at an infinite distance, allowing your eye's muscles to completely relax while reading, thereby effectively eliminating eye strain.

This is a simple project geared towards anyone who wants to build a librescope. A few basic materials are required, all of which (minus the 3D printer) should cost under or around $50.

1. 2x Double convex-lens with a diameter of 50mm and a focal length of 50mm (although I use a double-convex lens, plano-convex or even aspheric lenses with similar specifications will work even better, this is just a cheaper option).
2. 2x Double concave-lens with a diameter of 50mm and a focal length of -50mm. The lenses together are ~$40 with shipping here: concave, convex (this is the cheapest option I found after extensive searching).
3. 2x Small screw (I use M2-0.4x4.0) and corresponding screwdriver ~ $7 here: screws (I used the screws in the #10 box).
4. 3D printer or some other way to construct eyeglass frames (don't let the lack of a 3D printer discourage you! There are plenty of cheap 3D printing services online, and a cardboard or acrylic construction will work just as well).
5. Autodesk Fusion 360 (don't worry if you don't have Fusion downloaded, Autodesk allows hobbyists and students to use it for free and it's a very intuitive software. Now is a good time to learn how to use it!). Download it here.

Skip this section if you just want to get to the build, or if you don't want to understand how the physics work.

The human eye is one of the greatest optical instruments ever created, but it's not without its limitations. The eye functions by refracting light (refraction occurs when light rays bend after entering a different material, see this article for more information) onto the retina, which can be thought of as a sensor that converts light into signals the brain can use to construct an image. Most of the refraction occurs at the outer surface of the eye, but some occurs at the lens, which is a transparent tissue that is stretched and relaxed by the ciliary muscle (yes, there are muscles in the eye! I bet you'll never skip eye day again). The stretching and relaxing of the lens is what allows us to focus on objects at different distances.

When we view an object further than 6 metres (20 feet), the lens is essentially completely relaxed. When we focus on objects closer than that, the ciliary muscle must stretch the lens. The average distance at which a person reads a book is around 40 centimetres (16 inches), which is much closer than the relaxed viewing distance, and can result in asthenopia, or eye strain. Test this by looking at a screen or book, and then looking at a far off object. Focusing on the far object feels more relaxed.

A traditional telescope "projects" the image of an object at a distance of infinity, allowing the viewer to be completely relaxed as they regard celestial objects. If this technology could be applied to reading glasses, eye strain from reading could be completely eliminated. This technology would have greater implications for reducing vision problems as a whole, as near work (focusing on close objects like a book or computer screen) can cause temporary or permanent myopia, especially in children. Furthermore, those with weaker ciliary muscles, like the elderly, cannot focus on near objects. This technology could allow them to read again. Thankfully, using physics and elbow-grease, we can apply this technology to reading glasses!

A lens works by accepting light from an object and refracting it so that, when you look through the lens, the object appears to be at a different place. For example, when looking through a magnifying glass, the object (whatever you're looking at through the glass) appears to be much closer to your eye than it is (see image above). This "new position" is called the image of the object. The location of the image of an object looked at through a lens can be predicted with the following equation, called the Thin Lens Equation: 1/f = 1/p +1/q, where f is the focal length of the lens (the distance from the centre of the lens to the point at which the lens focuses light), p is the position of the object measured from the centre of the lens, and q is the position of the image measured from the centre of the lens. By convention, the object must be on the left side of the lens and the image on the right, or else the corresponding variables become negative.

When two lenses are placed next to each other, the image from the first serves as a "virtual object" for the second. This can allow for interesting lens combinations to achieve various optical effects. One consideration, however, in making a multi-lens system is image magnification. The magnification of an image is defined as the ratio of the image height to the object height, or the fraction -q/p. If the magnification is negative, the image is inverted. If it is greater than one, the image is larger, and if it less than one it is smaller.

The goal for the librescope is to create a system of lenses that places the final image of the book near negative infinity (so that it appears in front of the lenses) without making it appear smaller or inverted. Since infinity is difficult to work with, mathematically, it is necessary in this case to calculate angular magnification. Angular magnification refers to the ratio between the angle subtended by the image and the eye and the angle subtended by the object at the near point and the eye without the use of a lens. In other words, it's the ratio between the angle formed when you draw a line from your eye to the top of the object when it is placed at 25 cm (the closest distance at which most people can resolve details on an object, and the distance at which an object appears largest when our eye is unaided), and the angle formed when you draw a line from the top of the image formed by the lens to the eye. Mathematically, it ends up being defined as arctan(h/p)/arctan(h/N) for a single lens, where h is the height of the object, and N is the near point, or 25 cm. For two lenses, the angular magnification for both must be calculated and then multiplied to find the final magnification.

Using the Thin Lens Equation, I made the above graph, showing object (the book in this case) distance on the x-axis and image location on the y-axis. As you can see, the vertical asymptote is 0.4 m, as it should be. After this, the image actually makes the book appear closer, but it never places it closer than around 30 cm.

For practical purposes, two lenses is the maximum for this project, as any more will result in a too bulky frame and other issues. Let's collect the variable we already have from Step 2: p1 = 0.4 m (remember, most people hold a book at 40 cm (0.4m)), q2 = -∞ m. The "1" and "2" behind the variables refer to the lenses they correspond to. The book will be the object for the first lens, and the final image will be from the second lens. f1 and f2, the focal lengths of the two lenses, are up to us to choose. For the first, let's go with 5 cm, as this is a commonly available focal length. Using the Thin Lens Equation, we can calculate the location of the image: q1 = 1/(1/f1- 1/p1) = 1/(1/0.05 - 1/0.4) = 0.0571 m, or 5.71 cm. This means that the image will appear about 6cm to the right of the first lens.

We can use this image as the object for the second lens, which will be separated by some distance d (measured from the centres of both lenses) from the first lens. We want the lenses to be relatively close, ideally within 1-2 cm, as otherwise the librescope would be too bulky, and no one wants to wear an actual telescope on their face. So, for the second lens, the virtual object will be on the right side of the lens, making p2 negative. The exact distance will be p2 = -(q1 - d). We can use this, along with -∞ for q2 and a focal length, f2, we choose to solve for the lens separation d. For f2, let's choose -5 cm (negative focal length because it's a concave, or diverging, lens) because it corresponds to the first lens and therefore seems like it wouldn't cause too much size distortion of the image (we'll check with the math later). Plugging these values into the Thin Lens Equation for the second lens, we get 1/f2 = 1/-(q1 - d) + 1/q2, which becomes d = 1/(1/f2 - 1/q2) + q1 = 1/(1/-0.05 - 1/-∞) + 0.05714 = 0.00714 m, or 7.14 mm, almost 1 cm. Perfect! That will allow for some space between the lenses, but not too much.

To solve for the magnification, let's begin with the first lens, using the height of text on a page (3 mm or so) for h: m1 = arctan(h/p1)/arctan(h/N) = arctan(0.003/0.4)/arctan(0.003/0.25) = 0.625. This means that the first lens will create a smaller image. Using the linear magnification equation M = -q/p, we find that the image is actually inverted, so we will treat this angular magnification as negative. To solve for the second lens, we must use p2 = f2, as to create an image at infinity, the object must be at the focal length of the lens. Plugging this into the magnification equation: m2 = arctan(h/f2)/arctan(h/N) = arctan(0.003/-0.05)/arctan(0.003/0.25) = -4.99.

Multiplying these two magnifications gets around 3.13, meaning that the final image will be magnified slightly (3x isn't as large as it seems, but it will make the text appear larger and more comfortable to read) and upright. Perfect!

This will be the most involved step, but I'll walk through it step-by-step with beginners in mind. There's no better time than the present to learn how to use Fusion 360!

One note: because glasses are a wearable, you may want to make all of the following dimensions into parameters (click the fx symbol under Solid in Fusion 360. Making a parameter allows you to change a dimension after it's been used). This will allow you to change the glasses at will so that they conform to your head shape and preferences.

While you can go for any aesthetic you desire, I opted for thin circular frames (not just so that you can look like Harry Potter while reading Harry Potter, but that's an added plus) because they fit the shape of the lens best.

Begin the design by making a sketch with a circle with a diameter of 50 mm. This will be the inner portion of the frame where the lenses rest. If your 3D printer has issues with dimensional accuracy, you may want to add in some room for tolerances. Create two offsets (you can use the offset tool under modify), each 1 mm, one outside of the 50 mm circle and one inside. The outer offset will form the shell of the frame, and the inner offset will serve as a retaining wall for the lenses.

Next we must make the nose bridge. Starting from the centre of the outer circle, make a line slightly slanted outwards. Connect the other end to horizontal line. Connect the end of this line to a line slanted downwards (the mirror-image of the first line). This should leave you with an angular arch of three straight lines. Adjust the lengths and height until it suits you. I chose the height to be 7.5 mm and the top horizontal line to be 12 mm long. In total, the lines should span a distance of around 20 mm. After making the arch, fillet the corners until the bridge is relatively smooth and arc-like. Once this is done, offset it by 2 mm towards the top of the arch. Depending on the strength of your printer filament, it may be necessary to add another line through the arch. The purpose of this line is to create areas at the edges of the bridge that can be extruded to provide extra support to the bridge.

Next make a rectangle that extends from the edge of the outer circle opposite to the bridge. Position its centreline so that it is even with the height of the bridge. Make the height of the rectangle 4 mm and the width 10 mm. Attach it to the edge of the outer circle and fill in any missing area with a line connecting the top-right corner rectangle to the circle. This geometry will serve as a connector to connect to the temple arms.

Make a construction line (a dotted line, this is an option in the line dialogue that appears when you click line on the toolbar) through the exact centre of the bridge and mirror the connector and circles over the line using the mirror tool under create. Refer to the above drawing for dimensions and a reference for what the final frame sketch should look like.

Click the middle circle (it should be 1 mm wide, not the largest circle and not the outermost circle) and extrude the back side by (in mm) 0.5 * (7.143 (the lens separation) + 4 (the width of the concave lens) + 3 (the width of the convex lens) ) - 4 (the width of the concave lens again). Extrude the front side by 0.5 * (7.143 (the lens separation) + 4 (the width of the concave lens) + 3 (the width of the convex lens) ) - 3 (the width of the convex lens again). Now the wall which separates the lenses is complete.

Click the outermost circle and extrude both sides by 0.5 * (7.143 + 4 + 3 ) (same pattern as above). The lens portions of the frame are complete.

Click the bridge area and extrude both side by 3 mm. Don't forget to include the strengthening areas.

Extrude both arm connector areas (the rectangles at the edges of the frame) by 1.5 mm on each side (although I found the connectors to be somewhat fragile when I printed my librescope, so it may be wise to thicken them a bit).

Make a sketch using the back face of the arm connectors as your sketch plane (the plane on which you can draw sketch objects). Use the project tool (or press p) under create and click on both arm connectors. These include their edges in the sketch so that they can be referenced. Using the outer corners of both, make a rectangle with a width of 3 mm. This will allow us to extrude a vertical component of the arm connectors.

Once this is complete, extrude both rectangles by 13 mm. Make a sketch using the inner face of the right vertical portion of the arm connector. Project it into the sketch as before. Make a 4 x 4 mm rectangle that is partitioned horizontally down the middle. This will be the base of the hinge that allows the arms of the librescope to fold in. Extrude the lower half by 4 mm. Repeat the preceding steps for the left arm connector.

Make a sketch using the top of the rectangle you just extruded as the sketch plane. Project it into the sketch. Using a construction line, connect two opposite corners. Place a point (under create) at the midpoint of the line (it should snap to the midpoint when you hover over the centre of the line. Repeat this for both rectangles you just extruded. Finish the sketch and click the hole tool under create. Make two holes hole centred on each point that are threaded so that they can accept M2x0.4 screws (this is an option in the dialogue). Make the holes go through the entire rectangle.

Extrude the other half of the horizontally-partitioned rectangle through the arm connector so that it cuts it completely. Except for final touches, the frame is now complete!

Make a sketch using the outer face of the arm connector as the sketch plane. Project the connector face into the sketch. Starting on the upper-left corner of the larger rectangle (not the smaller, half-rectangle), make a horizontal line 85 mm long. Do the same starting on the lower-left corner. Starting from the end of the upper line, make two construction lines: one horizontal and 50 mm long, and the other, originating from the end of the horizontal construction line, vertically downwards 30 mm.

Make a spline using the fit point spline tool under create and place 5 points. One on the end of the upper horizontal line, three in a gentle arc downwards, and the last on the end of the vertical construction line. Make another spline originating from the end of the other horizontal line, and place four points in a gentle downwards arc and one on the end of the vertical construction line. Adjust all the points until the splines create an eyeglasses-like arm that starts thin and gets thicker towards the bottom.

Extrude the area you just made 3 mm inwards.

It's worth noting that when I printed my librescope, it tended to slip off my face. It may be wise to steepen the ear curve section of arms more than I did so that it doesn't slip off as easily.

Extrude the top rectangle of the horizontally-partitioned rectangle from before so that it joins with the arms and not the frame (you may have to toggle the visibility of the frame off for this). Extrude it 4 mm.

Make a sketch using the top face of the arm as a sketch plane and project it. Like before, make a construction line connecting two opposite corners of the 4 mm x 4 mm rectangle and place a point on the midpoint. Make a hole centred on this point with a countersunk head area 3 mm in diameter and a straight (non-threaded) inner hole of 2 mm all the way through the rectangle.

Make a plane along path (under construct) using the horizontal bridge line as the path. Type 0.5 into the dialogue so that the plane is centred on the line. Mirror the entire right arm over the plane to create the left arm. Now all that's left is filleting!

Fillets are largely up to your discretion, but I added some on almost every outer edge and corner. It requires experimentation to get some of them right, but the only fillets that truly matter are those the provide structural support to the hinge, as pictured above.

I also changed the material of the frames to black plastic (under modify, physical material) for aesthetic purposes, and added hinge joints to the arms and frame (this isn't necessary, but if you're curious, check out this site).

Now that we've done the math and design the librescope, it's time to actually create it! I used standard 3D PLA settings to print the librescope (20% infill, supports, 50 mm/s print speed, and a skirt for bed adhesion) and it printed well. After 3D printing the files found below, use M2 screws to attach each temple arm to the corresponding side of the lens frame. The tighter the screw is, the more resistance you'll feel when folding the arms. As the plastic can be fragile, take care not to break the hinge when you do this. If you do, don't worry! A spot of glue should hold it together.

After assembling the arms, place the lenses into the frame. Make sure the lenses are clean of all fingerprints and grease. They'll be fairly inaccessible after they are placed in the frame. Place the convex (outward-curved) lenses on the side of the frame opposite the arms, and the concave lenses on the side of the frame with the arms. Although the frame is meant to tightly secure the lenses, it may be necessary to use some hot glue or superglue to hold the lenses in place.

And that's it! The assembly is complete and the librescope is finished.

Test the librescope by looking through it, focusing on the text of a page 40 cm away, then quickly taking it away. You'll notice that your eyes have to refocus to look at the text unaided. It should feel more strained without the librescope on. The librescope should slightly magnify the text on the page or screen, and when it is moved more the 40 cm away from an object, the object should become blurry and difficult to focus on.

Now let's address the aberration in the room: spherical aberration occurs when spherical lenses are used (disregard this if you used aspherical lenses), and causes the image at the edge of the lens to be blurry and unfocused. It happens because light entering at the very edges of a spherical lens focuses at a slightly different place than light closer to the middle of the lens. This cannot be easily fixed without buying expensive aspherical lenses. The librescope isn't majorly affected by spherical aberration, but it could cause the edges or middle of the glasses to be slightly blurry. To try to ameliorate this at least a little, experiment with reducing the aperture of the lenses by putting opaque tape around the edges or covering them some other way. This blocks some of the light that focuses at incorrect points.

When I assembled my librescope, the frame proved too heavy and caused it to slip from my face. On the next iteration, I'll make the part that fits around the ear steeper and longer and the issue should be addressed. Alternatively, weights could be attached to the arms to counterbalance the lenses. If I were to make another iteration, I would also strengthen the arm connector and the arms, which are fragile.

*Image Source: https://en.wikipedia.org/wiki/Spherical_aberration#/media/File:Spherical_aberration_2.svg

Curl up with your new librescope and a good book and read to your heart's content! Eye strain won't stop you now.