lenses and apertures

lenses and apertures

Photo Demonstration

Depth of field

Depth of field (DoF) is one of the most important concepts in photography. Many photographers know that you can control DoF by adjusting aperture.

Depth of field is the distance between the closest and farthest objects in a photo that appears acceptably sharp. Now your camera can only focus sharply at one point. But the transition from sharp to unsharp is gradual, and the term acceptably sharp is a loose one!

Scientifically, it is based on something called the circle of confusion. This involves more physics than I’m going to get into here! In these two sketches, I have tried to illustrate what is meant by a narrow and large DoF. In a photograph with a narrow DoF, only a small slice of the image is in focus. Conversely, with a large DoF, much more of the scene is sharp.

There is one specific distance at which the lens focuses. This distance (called the focus distance) can be adjusted. Whenever a point is further away from the lens than this unique focus distance, its light rays don’t focus on the sensor any more, but intersect somewhere in the air in front of the sensor. These light rays again diverge after their crossing point, ending up as a blurred circle on the sensor. Similarly, when an object is closer than the focus distance, the corresponding light rays hit the sensor before they converge, also forming a blurred circle on the sensor.

Perspective

Humans view the world through their eyes which have a constant focal length of approximately 22mm f/2.1, but has an effective focal length of 43mm.Foreshortening plays a big role in art, and has been extensively studied over the ages. Artists originally only needed to learn the way in which distant objects appear smaller to a human observer.

Our camera gear gives us the opportunity to change focal length. Essentially, longer focal lengths reduce the relative differences in size between a subject and the distant background, whereas wide angles exaggerate this difference.

Focal length and sensor size influence a camera’s field of view: a shorter focal length or a larger sensor equals a larger field of view. To make the main subject fill the same fraction of the second photograph we had to move the camera closer. A change in distance between the camera and the subject(s) changes the camera’s perspective, i.e. the relative sizes of the subjects in the photograph.

Aperture

Aperture is the opening in your lens that lets light pass through to the sensor. Think of it as a pupil(瞳孔) for your lens. It dilates(扩大) to let more light in, and contracts to restrict light when it is bright. Aperture is probably the first thing most photographers think of when they want to adjust the depth of field.

Large apertures, which correlate to small f-stop numbers, produce a very shallow depth of field. On the other hand, small apertures, or large f-stop numbers, produce images with a large depth of field.

Captured with a NIKON D800 and 24-70mm f/2.8 lens @ 24mm, ISO 200, 8/10s, f/22.0 This image has a large DoF. I focused on the rocks about 5m ahead of me. The foreground rocks and the distant clouds are all in focus. Captured with a NIKON D500 and 17-55mm f/2.8 lens @ 22mm, ISO 200, 1/1600s, f/2.8 This image has shallow DoF. Here I focused on the boxing gloves. They are sharp, but the background is blurred.

Camera-Subject Distance

Another important factor affecting depth of field is the distance between the camera and the subject. The shorter that distance, the smaller the depth of field. Have you ever tried to take a close-up shot of a flower or insect, but can’t get the entire subject in focus, even with a small aperture? This is because the closer you are to your subject, the shallower the DoF.

Look at these two sets of images. The camera-subject distance in the first group of pictures is 1.5m. After each shot, I stopped down the aperture. The second set has a focus distance of just under a half a meter. Notice two things. In each set of pictures, as the aperture narrows, the DoF increases. In addition, for each pair of photos shot at the same aperture, there is more depth of field when the camera-subject distance is greater.

Focal Length of the Lens

Wide-angle lenses (short focal lengths) have a deeper depth of field than telephoto lenses (long focal lengths). Well, not exactly! It isn’t quite as cut and dry as that. If you take an image and do not change the camera-subject distance, this is true. You can see this illustrated in these two sets of images below. The top set is shot at a focal length of 70mm. The bottom set at 105mm. Both sets were taken at a distance of 2m from the subject. Notice how for each pair of images shot at the same aperture, the DoF is larger for the narrower focal length lens.

However, it isn’t fair to compare these two sets of images. The field of view in each collection is very different. The top group of images has taken in much more of the surroundings, and the reindeer are much smaller in the frame.

To make the comparison fair, I took two more shots. The first was taken at a focal length of 35mm and approximately 0.6m away from my focus point (still the eye of the nearest reindeer). For the second image, I moved the camera back, so it was 1.2m away from the subject. Then I zoomed into 70mm and framed the shot so that the head of the deer was approximately the same size and location as in the first shot. It turns out the DoF in both these images is the same. You can see this looking at the acorn in front of the deer’s nose and the snowflake and acorn just behind the nose. In both images, they are equally sharp.

So why do the two shots look different? Well, two reasons. The first has nothing to do with depth of field. I’m afraid that while I was composing and shooting, the sun went down! So, you must ignore the fact that the background is darker in the second photo. I do apologize for this! Apart from that, the difference lies in the fact that the longer focal length has a narrow angle of view. Thus, a smaller portion of the background fills the frame. The apparent magnification of the background gives the sense that the blur is larger in the photo shot with the longer lens. My article “What is Lens Compression and How to Use It In Your Photos” talks about this in more detail.

So focal length does not actually influence DoF if you adjust the camera-subject distance so that the magnification of your subject is the same.

Sensor Size

In a nutshell, cameras with smaller sensors have larger depths of field. However, you have to be careful how you make the comparison. You must look at cameras with lenses that have the same effective focal length so that the fields of view are the same. If you shoot at the same camera-subject distance, with the same apertures, you will find that the larger sensors have a shallower DoF. That is why many professional portrait photographers like to use full frame cameras. Here is an example. A full frame camera with a 120mm lens, an APS-C camera with an 80mm lens, and a Micro 4/3 camera with a 60mm lens (all the same field of view) are each set to an aperture of f/9 and a camera-subject distance of 5.0m. This table summarizes how the DoF will look in each image.

A common question though is can you take similar images, with the same DoF’s, using cameras with different sensor sizes? The answer is yes. However, you must divide the apertures by the crop factor in order to get the same depth of field. Using the same cameras and lenses in the above example, but setting an aperture of f/18 on the full-frame camera, f/12** on the APS-C sized sensor and f/9 on the Micro 4/3 camera, you will end up with images that not only take in the same field of view but have approximately the same DoF.

Circle of Confusion

As we saw from the light ray diagram above, there is only a single distance at which even an ideal lens will focus the image perfectly. A point source at any other distance is blurred to a circular blob on the image plane that is called the circle of confusion (CoC). In practice, however, there is a range in which the CoC is imperceptible, as your eyes aren’t good enough to tell that the light is blurred to form a non-zero-sized disc. The transition from imperceptible to perceptible blur varies from person to person but on average subtends an angle of approximately 1 arc minute, as seen from your eye.

Now we can define Depth of Field: it is the region where the CoC is less than a certain value, i.e. where the entire image or a particular area of the image is perceived to be “sharp enough”. Depth of field is therefore based on some definition of “acceptable” sharpness and is essentially an arbitrary specification. The CoC cut-off size that defines depth of field ultimately depends on the resolution of the human eye, as well as the magnification at which the image is viewed.

At normal reading distance 1 arc minute represents a diameter of about 0.063 mm on a piece of paper – about as wide as the thickness of a human hair. Interestingly, the photographic community long ago and for some unclear reason decided that they will instead settle for a coarser limit to the circle of confusion, roughly 0.167 mm, which means you might find depth of field scales printed on some lenses to be a bit over-optimistic. These DOF scales are therefore more a crude rule of thumb than anything useful.

Field of View

crop factors

Graphic compute

The reason we have defocus blur in real cameras is because they need a big hole (rather than just a pinhole) through which to gather light.

focus distance : the distance between the camera center and the plane where everything is in perfect focus the focus distance.

focus length : is the distance between the camera center and the image plane.

For our model, however, these two will have the same value, as we will put our pixel grid right on the focus plane, which is focus distance away from the camera center.

The “aperture” is a hole to control how big the lens is effectively. For a real camera, if you need more light you make the aperture bigger, and will get more blur for objects away from the focus distance. For our virtual camera, we can have a perfect sensor and never need more light, so we only use an aperture when we want defocus blur.

A Thin Lens Approximation

usually start rays from an infinitely thin circular “lens”, and send them toward the pixel of interest on the focus plane (focal_length away from the lens), where everything on that plane in the 3D world is in perfect focus.

In practice, we accomplish this by placing the viewport in this plane. Putting everything together:

• The focus plane is orthogonal to the camera view direction.
• The focus distance is the distance between the camera center and the focus plane.
• The viewport lies on the focus plane, centered on the camera view direction vector.
• The grid of pixel locations lies inside the viewport (located in the 3D world).
• Random image sample locations are chosen from the region around the current pixel location.
• The camera fires rays from random points on the lens through the current image sample location.

Without defocus blur, all scene rays originate from the camera center (or lookfrom). In order to accomplish defocus blur, we construct a disk centered at the camera center. The larger the radius, the greater the defocus blur. You can think of our original camera as having a defocus disk of radius zero (no blur at all), so all rays originated at the disk center(lookfrom).