The rows are marked with numbers from 1 to as many as the breadboard design has. The columns are marked with A, B, C, D, E on one side of the board, and F, G, H, I, and J on the other side. Only five components can be connected in each row.

Conic Constant (k): Defines the section of a conic to use as the base of the asphere. If k > 0 the surface is an oblate ellipse, k = 0 is spherical, -1 < k <0 is a prolate ellipse, k = -1 is parabolic, and k < -1 is hyperbolic. Occasionally, a design will specify eccentricity instead, in which case k = -e2.

Make sure to push them all way through, until they can’t go any further. A lot of beginners will push the legs partially into the breadboard, not wanting to break them. This can, in turn, lead to strange circuit behavior, like LEDs flickering or not working at all, etc. The components can get damaged this way, so it’s always better to firmly push them down all the way.

Last but not least, a mini breadboard is 4.6 cm tall and 3.6 cm wide (1.8” x 1.4”). It has 170 tie-points and doesn’t come with the power strip. It’s perfect for small and simple projects. It fits nicely on top of the Arduino proto shield as a small circuit. It is then used as a signal source feeding other electronic circuits. Mini breadboards come in various bright colors, but they are the same no matter the color.

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As with any other product, there are pros and cons to using a breadboard. Let’s take a look at why you would consider using it, and why not.

Many integrated circuits (aka ICs or chips) are developed to fit onto breadboards. Since they tend to be larger than other components, they come in the so-called dual in-line package (DIP or DIL). That minimizes the amount of space they take on the breadboard. The ICs fit perfectly over the ravine. One side of the legs connects to column E, and the other side connects to column F. This way the legs of the ICs don’t interfere with each other’s functionality.

U-shaped wires are simply wires with insulation stripped at both ends and bent at a 90-degree angle. Unlike Dupont-style, these wires keep their shape once they are put in position. They are great for connecting to power and ground since they keep the connection as short as possible.

Sag: Height difference, in ‘z’, from the vertex of the asphere to the point in question. The usual sign convention is for a convex surface to have positive sag, but this is not universal.

Future installations of this blog series will expand on many of the topics covered in this introduction. Check back frequently for updates!

At the very center of the breadboard lies a small ravine. It serves an important purpose. It is 7.6 mm (0.3 inches) wide and enables the usage of integrated circuits.

Areaspheric lensesbetter

Keep in mind that some components have very long legs that don’t fit into the breadboard all the way. LEDs are like that. Be careful not to break them when putting them in. You’ll feel it when the component hits the bottom of the breadboard. The connections are not permanent and it’s easy to remove any components that might be connected wrongly.

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Components have long metal legs called leads used to get the electrical current to the component. Just put these legs through the holes and that’s it! The metal clips below will grab onto them and make them electrically connected to anything else in that row.

An aspherical lens is any lens that has an optical surface that is not spherical and may include cylindrical, toroidal, and general freeform surfaces.

Forbes Polynomials: An alternative to the traditional asphere equation. Forbes polynomials, Qcon and Qbfs, have characteristics that aid in design for manufacturability. Not all processing and metrology tools support these equations.

The main areas, those between the power rails, are used to hold most of the electronic components. As power rails, terminal strips are also divided into two columns, with a small ravine between them.

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The constantly changing curvature of the aspheric surface allows the optic to correct aberrations in the optical system more efficiently than spherical lenses. As a result, this allows a more compact and lighter optical train by reducing the number of components needed and improving the overall correction of the system. Cost tends to be the trade-off for using aspheres because they are typically more expensive to manufacture than traditional spherical lenses due to the specialized knowledge and technologies required.

A solderless breadboard is as simple a device as it gets. It’s the most used device when creating temporary circuits. It is called solderless because no soldering is required, you can just plug in the components. A component can easily be removed from a breadboard if you make a mistake, or when starting a new project. This makes it great for both beginners who are just starting to learn about electronics and seasoned professionals.

Looking at the breadboard from the top side, you’ll see a bunch of little holes. This is where the legs of components go, and the clips inside grab on them. The spacing between these holes is 2.54 mm (0.1 inches). It is aligned with the spacing between the legs of most electronic components and integrated circuits.

In precision optics, the term asphere generally refers to an optic in which the local radius of curvature of an optical surface changes from the center, of its optical axis, to the edge and is rotationally symmetrical about the optical axis. We will be using the above definition for this blog series. Several methods and equations describe these aspherical surfaces, with the most common equation being the conic and polynomial general asphere equation (see below) and Forbes polynomials (Qcon and Qbfs).

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Below is the general asphere equation where z is the surface sag, x is the distance from the center, k is the conic constant, R is the base radius, and A# is the polynomial expansion terms.

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Manufacturing challenges arise from the ever-changing local radius of curvature of the aspherical surface that prevents traditional spherical tools and techniques from being used to grind, polish, and measure these surfaces. The tools used for aspheric production are single point or sub-aperture, which means they only process a small portion of the lens at any given time. As a result, this increases the processing time and allows only a single lens to be ground or polished at a time. Depending on quantities, material, and geometry, it may also be possible to mold or diamond turn an aspheric lens.

Disadvantages ofaspheric lenses

To connect the components to each other, Arduino or a power source, we’ll need some wires. Jumper wires are a type of wires that are used with the breadboard. There are two types most commonly used: Dupont-style and U-shaped.

Profilometer: Metrology equipment for aspheres that measures a single point at a time while scanning the surface. The most basic profilometer measurement is a single trace from one edge to the other, through the vertex. Some profilometers can do raster or spiral scans to obtain a full map of the surface error. Profilometers may contact the surface with a stylus or may use a non-contact method.

As it usually is with technology, the breadboard of that time has evolved over the years. While breadboards are now used for all kinds of electronics prototyping, they aren’t made from wood anymore. You no longer have to ruin cutting boards every time you wanted to test something. The name, however, stuck and reminds us daily how far we’ve come in just a few years.

The most common size among beginners is the so-called half-size. It is 8.5 cm tall and 5.5 cm wide (3.4” x 2.2”). As you can see, it’s basically the full-size breadboard cut in half. It has 400 tie-points, or 30 rows and 10 columns. It has removable power rails. Removing them makes the board 3.5 cm (1.4”) wide.

If you’ve never worked with it before, you might wonder which holes do what. Let’s take a look at the bottom of a breadboard so you get a better idea of what’s going on.

Seeing it like this, you’ll get a better picture of how it works. The smaller metal platings are used for connecting components into your circuit. Rows are not interconnected. Two larger metal platings, perpendicular to smaller ones, are used to connect the board to a power source. That’s why they are referred to as power strips or rails (sometimes called bus strips).

Power rails generally go from one end of the breadboard to another. The holes are set in groups of fives. On large breadboards, however, the power rails are often broken in two.

Departure: Difference between the theoretical sag of the aspheric surface and the BFS. This may be used to refer to the maximum departure on the asphere or just a specific point. The departure is measured in the ‘z’ direction, not normal to the surface.

If you’ve got a starter kit for an Arduino or Raspberry Pi, you probably have one. And you’ll be using it quite a lot. Let’s take a deeper look at what they actually are.

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If you were to take the metal platings out, you would see that they are actually little metal clips. They’re designed to grab the legs of components pushed through holes on the top side of the breadboard. Because they’re made from a conductive metal, you can test circuits without any soldering. Hence, the name solderless. All breadboards operate like this, no matter the size.

As shown in the below image, a spherical (left) and aspherical (right) lens focusing on a collimated beam of light. For the spherical surface, the light entering near the edge is focused closer to the surface than the light entering near the center. This creates a large spot size, which reduces, for example, the power density of a laser spot. The varying radius of the aspherical surface allows the lights entering the edge and center of the lens to be in focus at the same point.

SMD components are better in almost every aspect compared to their leaded counterparts. The problem with them, though, is that there is no easy way to directly prototype with them without making a PCB  to mount them to. Because of this, many SMDs will continue to be adapted for breadboards. You don’t have to worry about fabricating a PCB every time you want to work with a circuit for the foreseeable future. The breadboards are not going anywhere.

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Best Fit Sphere (BFS): Most commonly refers to the radius of the sphere which intersects both the vertex and the edge of the aspheric surface over a given aperture (e.g., the edge of the optic or the clear aperture). It is aperture-dependent so it is a good practice to specify the aperture when referring to the BFS. It can also be used to refer to the spherical radius that is the closest fit to the asphere without crossing the aspheric surface. For many aspherical designs, those with only positive departure, this is the same as the sphere that intersects the center and edge. BFS may also be used to refer to the sphere which has the smallest absolute departure or volume of removal from the asphere.

Now that we have an understanding of what a breadboard is, it’s time to learn how to use it. You’ll be able to put most components on the board.

Dupont-style wires come in three varieties, depending on their ends: male/male,  male/female, and female/female. They are very flexible and easy to work with, which is why they are often included in starting kits. For connecting an Arduino with a breadboard, a male/male Dupont-style jumper wire is used.

When just looking at the bullet points, it wouldn’t be unjustified to think you shouldn’t use a breadboard. The cons list is longer, after all. But pros outweigh the cons in this situation. The breadboard is just too useful for it not to be used in most cases. Unless you’re making a large project or something that must stay connected at all times, you can stick to using a breadboard for your projects.

Both types of wires come in different colors, but they don’t mean anything. There are some color-coding disciplines that you can adhere to for consistency, though. For example, you can use red and blue or black for supply voltages and ground. Use a different color for the main signals, and the rest how you see fit. There’s a common issue with this, though. The number of colors is often smaller than the number of signal types or paths.

Base Radius (R): The radius used in the aspheric definition. This is the same as the vertex radius unless an A2 term is used (strongly discouraged).

…an actual breadboard! Back in the olden days, amateur makers used to hammer nails or screws on a wooden board. They would then put copper wires on them and solder electronic components to them. Often it was literally a board used to slice bread on.

Power strips (bus strips) are on the sides of the breadboard. They are used to provide electric power to the electronic components. They usually contain two columns – one for ground and one to supply voltage. The row indicating ground is normally marked blue or black, while the row indicating voltage supply is marked red. Along with colors, a ground column is indicated with a minus (-), and a voltage column is indicated with a plus (+).

Speaking of sizes, while the half-size board will be sufficient for most of your needs, you might consider getting a different-sized breadboard. A full-size breadboard  is 17 cm tall and 5.5 cm wide (7” x 2.2”). It has 830 tie-points (holes), or 63 rows and 10 columns. Pulling out the power rails narrows the breadboard to just 3.5 cm (1.4”). It usually has tabs and notches so you can make it longer and wider.

Once a designer has decided that one or more aspheric surfaces would benefit the optical system, some manufacturing and tolerancing considerations should guide the design process to ensure manufacturability and testability. These include both geometric attributes of the lens (e.g., local curvature) and design parameters (e.g., optimization diameter of the lens).

Gullwing: An extreme case of an asphere with an inflection point where not only does the local radius change sign but the sag turns back on itself.

Breadboards come in all shapes and sizes, but they are pretty much all the same. They are made from plastic and come in different colors, but they are usually in some tint of white. The most common sizes you’ll see are so-called full-size, half-size, and mini. Most breadboards have tabs and notches so you can snap more of them together. For the most part, though, you’ll be fine using just one half-size board included in most starter kits.

As shown below, this is a before and after image of adding an asphere in an optical system. Performance with an asphere is maintained while having fewer elements and a more compact system.

Aspherical lens photography

Inflection Point: A point on the asphere where the local radius changes sign, e.g., from a convex to a concave radius. This may increase the difficulty of manufacturing and measuring the asphere.

Local Radius: Radius of curvature at a given location on the asphere. Unlike a spherical surface, the local radius is constantly changing on an asphere.

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A breadboard is a construction base for electronics prototyping. It might look like a regular plastic board with many tiny holes in it, but it’s much more than that. It is one of the main tools for circuit building and electronics in general. Prior to today’s breadboard being invented in 1971, a technique called wire-wrap was used for circuit building. It involved wrapping wires several times around a component lead or a socket pin on an insulating board. You had to be really careful and know what you were doing. Things could get messy quite quickly, as you can see from the picture below.

If you want to make an electronics project, you will need something to connect your circuit on. Sure, you could solder everything together, but what if you’re just testing something? Or if the project you’re working on is temporary, and you plan on using the parts for something else? You would then use a breadboard.

Wait, the row has ten holes, so why can you connect only five components? Notice that each horizontal row is separated by a ravine, or crevasse, in the middle of the breadboard. This ravine isolates both sides of a given row from one another, and they are not electrically connected. Thus, a hole on one side is not electrically connected to a hole on the other side.