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Numerical apertureand resolution
The refractive indices of the core and cladding, ncore and nclad , respectively, play a key role. In order for TIR to occur, ncore must be larger than nclad . The greater their difference, the larger the NA and maximum acceptance angle.
Figure 1: Rays incident at angles ≤θmax will be captured by the cores of multimode fiber, since these rays experience total internal reflection (TIR) at the interface between core and cladding. A requirement for TIR is that ncore > nclad .
Wider aperture, when applied at a distance (physically, or with a shorter lens) from the focal point, results in an apparent deeper depth of field than it does when it’s applied to a closer subject.
How to calculate numerical apertureof optical fiber
Deep depth of field is a great way to bring out detail in a large portion of the frame. Deep depth of field is commonly used in landscape photography to capture elements and textures in the majority of the frame throughout many vertical planes. To capture fine detail and deep depth of field, you should use a wide-angle lens to shoot at a distance and set your f stop at a high number for a small aperture.
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As a landscape photographer, you capture sweeping images of oceans capes, mountainsides, skylines, and wilderness. Your photos thrive on dramatic details viewed from close up and far away: Trees, birds, blades of grass are brought into focus to set the perfect stage.
Inversely, when you shoot the same subject at closer distance (physically, or with a closer focal length), you’ll notice a shallower depth of field.
Single mode fibers have only one guided mode, the lowest order mode, which is excited by rays with 0° angles of incidence. However, calculating the NA results in a nonzero value. The ray model also does not accurately predict the divergence angles of the light beams successfully coupled into and emitted from single mode fibers. The beam divergence occurs due to diffraction effects, which are not taken into account by the ray model but can be described using the wave optics model. The Gaussian beam propagation model can be used to calculate beam divergence with high accuracy.
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Simply explained, the term 'depth of field' refers to the area of an image that appears to be in focus. As the distance from the focal point increases, the focus gradually decreases until it appears to be out of focus. In any image, there’s a point of absolute focus and a corresponding region of the image surrounding the subject that appears to be in focus.
To gain a top-level understanding of how you can achieve shallow or deep depth of field by controlling aperture, here is a quick overview of aperture and its related elements: F-stop, shutter speed, and depth of field.
Numerical apertureformula with refractive index
Numerical aperture (NA) provides a good estimate of the maximum acceptance angle for most multimode fibers, as shown in Figure 1. This relationship should not be used for single mode fibers.
Referring back to the example in the introduction, landscape photographers typically want to capture a deep depth of field, where most of the image is in focus, from the foreground to the background. Portrait photographers typically want a shallow depth of field, where a smaller plane of detail in an image is sharpened, and any distractions in the background that may take away from the detail of the face are blurred.
Shallow depth of field is a great way to bring focus to a specific subject to separate it from its background. Shallow depth of field is commonly used in portrait photography and food photography. It is also great for action photography, such as sports and wildlife photography, because it separates the subject from their chaotic background and allows you to shoot with a quick shutter speed to capture crisp detail in action.
Learning to control depth of field will help you bring focus to the most important parts of your images and will greatly improve the technical and aesthetic quality of your photos.
Without getting too technical, it’s important to note that this apparent change in depth of field when applied at a closer or farther distance has everything to do with the portion of the frame that the subject fills. With magnified shots, less of the background is represented in the shot, and the blurred background is magnified, making the image appear to have a shallower depth of field. The inverse effect happens when an image is taken at a farther distance.
While distance plays a large role in depth of field, knowing how to adjust the f-stop to compensate for distance is often a much more convenient way to achieve your desired depth of field. This is especially true in landscape photography, where moving farther from a subject in any significant way is much more difficult than it is in close-up photography.
Numerical apertureunit
Single Mode Fibers are DifferentIn the case of single mode fibers, the ray model in Figure 2 is not useful, and the calculated NA (acceptance angle) does not equal the maximum angle of incidence or describe the fiber's light gathering ability.
Acceptance Angle and NAIn the ray model of light, a ray's angle of incidence determines whether or not it will be coupled into the fiber's core. The cutoff angle is the maximum acceptance angle (θmax ), which is related to the NA (Figure 1).
Angles of Incidence and Fiber ModesWhen the angle of incidence is ≤θmax , the incident light ray is coupled into one of the multimode fiber's guided modes. Generally speaking, the lower the angle of incidence, the lower the order of the excited fiber mode. Lower-order modes concentrate most of their intensity near the center of the core. The lowest order mode is excited by rays incident normally on the end face.
The aperture, as discussed above, is just one element of depth of field. The distance from you to your subject can change your perceived depth of field.
By following these tips outlined above, you should now be able to generally control your depth of field to take the images you want. The more you practice and experiment with aperture, distance, and focal length, the more you’ll be able to fine-tune depth of field in your images to enhance your individual photography style.
Aperture is not infinite; all lenses have their limits, which are clearly defined by the manufacturer. Manufacturers state a minimum and maximum range that the lens can be shot.
Figure 2: The behavior of the ray at the boundary between the core and cladding, which depends on their refractive indices, determines whether the ray incident on the end face is coupled into the core. The equation for NA can be found using geometry and the two equations noted at the top of this figure.
Depth of field is not equally distributed around the focal point. It is typically distributed unequally, with about 1/3 of the total field of focus lying in front of the subject, and two-thirds of focus lying behind the subject.
How to calculate numerical apertureof optical
Set your f-stop to a low number (for example, f/2.8). This will widen your aperture, and you will allow a lot of light into the lens. To compensate for the flood of light you need to shoot faster by adjusting your shutter speed. Your resulting depth of field will be shallow.
Rays with an angle of incidence ≤θmax are totally internally reflected (TIR) at the boundary between the fiber's core and cladding. As these rays propagate down the fiber, they remain trapped in the core.
Understanding depth of field is important and can greatly influence your photography; it helps distinguish the foreground from the background to create a focal point that draws the eye and tells it where to look. Knowing how to control depth of field gives you the opportunity to choose how much of (and what parts of) your image you want to bring into focus.
Numerical apertureof optical fiber
“Knowing how to control depth of field gives you the opportunity to choose how much of (and what parts of) your image you want to bring into focus.” - Mastin Labs
As a portrait photographer, you’re most concerned with photographing the unique, defining features of your subject; the bright sparkle in an eye, the freckles on a face, the tiny wrinkle in a chin. Images like this aren’t possible without understanding how to use depth of field (also known as focus range) to bring certain parts of your image into focus and blur out what’s less important.
Rays with angles of incidence larger than θmax refract at and pass through the interface between the core and cladding. This light may travel in the cladding for a while but is eventually lost from the fiber.
Set your f stop to a high number (for example, f/11). This will narrow your aperture, and you will let very little light into the lens. To compensate and to avoid having an underexposed image, you will need to shoot slower by adjusting your shutter speed. Your resulting depth of field will be deep.
If you shoot in anything other than a totally controlled environment, you have to know how to adjust your camera for the changing light. Aperture is the part of the lens that controls the amount of light passing through to the camera’s sensor, and its one of the simplest ways to control the depth of field. You can change the access of light by widening and narrowing the diameter of the opening through which light enters the camera.
If an image has a deep depth of field, it means its area of perceived focus is a broader and deeper portion of the image. If an image has a shallow depth of field, it means its area of perceived focus is limited to a narrower range.
Geometry Defines the RelationshipThe relationship between NA and θmax can be found using the geometry diagrammed in Figure 2. Snell's law was used at both interfaces, and the substitution sin(90°) = 1 was made. This geometry illustrates the most extreme conditions under which TIR will occur at the boundary between the core and cladding.