Category: Lenses

Most who are involved with imaging have at least some understanding of depth of field (DoF). DoF is the distance between the nearest and furthest points that are acceptably in focus. In portrait photography, one sometimes seeks a narrow depth of field to draw attention to the subject, while intentionally blurring the background to a “soft focus”. But in machine vision, it’s often preferred to maximize depth of field – that way if successive targets vary in their Z dimension – or if the camera is on a moving vehicle – the imaging system can keep processing without errors or waste.

Making it real

Suppose you need to see small features on an item that has various heights (Z dimension). You may estimate you need a 1″ depth of field. You know you’ve got plenty of light. So you set the lens to f11 because the datasheet shows you’ll reach the depth of field desired. But you can’t resolve the details! What’s up?

So I should maximize DoF, right?

Well generally speaking, yes – to a point. The point where diffraction limits negatively impact resolution. If you read on, we aim to provide a practical overview of some important concepts and a rule of thumb to guide you through this complex topic without much math.

Aperture, F/#, and Depth of Field

Aperture size and F/# are inversely correlated. So a low f/# corresponds to a large aperture, and a high f/# signifies a small aperture. See our blog on F-Numbers aka F-Stops on the way the F-numbers are calculated, and some practical guidance.

Per the illustration below, a large aperture restricts DoF, while a small aperture maximizes the DoF. Please take a moment to compare the upper and lower variations in this diagram:

If we maximize depth of field…

So let’s pursue maximizing depth of field for a moment. Narrow the aperture to the smallest setting (the largest F-number), and presto you’ve got maximal DoF! Done! Hmm, not so fast.

First challenge – do you have enough light?

Narrowing the aperture sounds great in theory, but for each stop one narrows the aperture, the amount of light is halved. The camera sensor needs to receive sufficient photons in the pixel wells, according to the sensor’s quantum efficiency, to create an overall image with contrast necessary to process the image. If there is no motion in your application, perhaps you can just take a longer exposure. Or add supplemental lighting. But if you do have motion or can’t add more light, you may not be able to narrow the aperture as far as you hoped.

Second challenge – the Airy disk and diffraction

When light passes through an aperture, diffraction occurs – the bending of waves around the edge of the aperture. The pattern from a ray of light that falls upon the sensor takes the form of a bright circular area surrounded by a series of weakening concentric rings. This is called the Airy disk. Without going into the math, the Airy disk is the smallest point to which a beam of light can be focused.

And while stopping down the aperture increases the DoF, our stated goal, it has the negative impact of increasing diffraction.

Diffraction limits

As focused patterns, containing details in your application that you want to discern, near each other, they start to overlap. This creates interference, which in turn reduces contrast.

Every lens, no matter how well it is designed and manufactured, has a diffraction limit, the maximum resolving power of the lens – expressed in line pairs per millimeter. There is no point generating an Airy disk patterns from adjacent real-world features that are larger than the sensor’s pixels, or the all-important contrast needed will not be achieved.

High magnification example

Suppose you have a candidate camera with 3.45um pixels, and you want to pair it with a machine vision lens capable of 2x, 3x, or 4x magnification. You’ll find the Airy disk is 9um across! Something must be changed – a sensor with larger pixels, or a different lens.

As a rule of thumb, 1um resolution with machine vision lenses is about the best one can achieve. For higher resolution, there are specialized microscope lenses. Consult your lensing professional, who can guide you through sensor and lens selection in the context of your application.

Lens data sheets

Just a comment on lens manufacturers and provided data. While there are many details in the machine vision field, it’s quite transparent in terms of standards and performance data. Manufacturers’ product datasheets contain a wealth of information. For example, take a look at Edmund Optics lenses, then pick any lens family, then any lens model. You’ll find a clickable datasheet link like this, where you can see MTF graphs showing resolution performance like LP/mm, DOF graphs at different F#s, etc.

Takeaway

Per the blog’s title, Depth of Field is a balancing act between sharpness and blur. It’s physics. Pursue the links embedded in the blog, or study optical theory, if you want to dig into the math. Or just call us at 987-474-0044.

1st Vision’s sales engineers have over 100 years of combined experience to assist in your camera and components selection.  With a large portfolio of lenses, cables, NIC cards and industrial computers, we can provide a full vision solution!

While a standard lens is adequate or even ideal for many machine vision applications, there is inherent distortion in a standard lens, often in the range of 1 – 2%. Telecentric lenses achieve distortion of 0.1% or less. They also provide constant magnification and no perspective error.

If you “just” need presence/absence detection, or counting discreet non-occluded objects, a conventional lens may be fine. But if you need highly accurate contactless measurement, telecentric lenses offer remarkable performance.

Let’s take a brief look at what qualifies a lens as telecentric, and why you might want (or need) one. Subsequently we’ll summarize Edmund Optics SilverTL^TM and CobaltTL^TM lens series.

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Telecentric Tutorial

Telecentric lenses only accept incoming light rays that are parallel to the optical axis of the lens. It’s not that the oblique rays don’t reach the outer edge of the telecentric lens. Rather, it’s about the optical design of the lens in terms of what it passes on through the other lens elements and onto the sensor focal plane.

Hmm, but the telecentric lens must have a narrower Field of View (FoV) – and I have to pay a premium for that? Well yes – and yes. There are certain benefits.

Let’s get to an example. In the image immediately below, labeled “Setup”, we see a pair of cubes positioned with one forward of the other. This image was made with a conventional (entocentric) lens, whereby all three dimensions appear much the same as for human vision. It looks natural to us because that’s what we’re used to. And if we just wanted to count how many orange cubes are present, the lens used to make the setup image is probably good enough.

But suppose we want to measure the X and Y dimensions of the cubes, to see if they are within rigorous tolerance limits?

An object-space telecentric lens focuses the light without the perspective of distance. Below, the image on the left is the “straight on” view of the same cubes positioned as in “Setup” above, taken with a conventional lens. The forward cube appears larger, when in fact we know it to be exactly the same size.

The rightmost image below was made with a telecentric lens, which effectively collapses the Z dimension, while preserving X and Y. If measuring X and Y is your goal, without regard to Z, a telecentric lens may be what you need.

Depth of Field can be “pushed”

You are likely familiar with Depth of Field (DoF), the range in the Z dimension in which objects in the FoV are in focus. With a conventional lens, if an object moves out of focus, the induced blur is asymmetrical, due to parallax (aka. perspective error).

But with a telecentric lens, there is no parallax error, since the FoV is constant and non-angular. A benefit of this is that even if the target image is somewhat defocused with a telecentric lens, the image may still be perfectly usable.

In the two images below, the “sharp transition” edge is clearly optimal. But when measuring tolerances in a manufacturing environment, with mechanized conveyors, vibration, etc., target objects may not always be ideally positioned. So the “shallow transition” image from the object just out of focus is entirely acceptable to identify the center of mass for the circular object, since the transition is symmetrical at all positions.

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Edmund Optics is widely recognized for their range of standard products – and their expertise in custom lens design when needed. The SilverTL^TM and CobaltTL^TM lens series each offer 10+ members, where all lenses are high-resolution and bi-telectric. Some additionally offer inline illumination options.

Noteworthy characteristics of both the SilverTL and CobaltTL series include:

• Aperture controls often not available in competitor products
• “Fast” ==> lower F# options than in many competitor products (so can work effectively with less light)
• Conform to narrowly specified engineering tolerances
• Pricing identical with or without in-line illumination via coax port

Edmund Optics SilverTL^TM series

The SilverTL series pairs with C-mount sensors up to 7.5 MegaPixels, ideal with 2.8 µm pixel size. Magnification options range from 0.16X to 4X.

Edmund Optics CobaltTL^TM series

For C-mount sensors up to 20 MegaPixels, and pixel size 2.2 µm, choose the CobaltTL series.

What type of lens is best for my application?

Machine vision is a broad field, with a lot of variables across wavelengths, application goals, sensor, software, and lens choices. If you are a seasoned veteran, you may know from experience exactly what you need. Or you may want to review our on-line knowledge base or online blogs. Easier yet – just phone us at 978-474-0044. You’ll speak with one of our sales engineers, who put customer success first. Customers with successful outcomes – who return to us project after project – is our goal.

1st Vision’s sales engineers have over 100 years of combined experience to assist in your camera and components selection.  With a large portfolio of lenses, cables, NIC cards and industrial computers, we can provide a full vision solution!