12 Lens Calculator

Milestone White Paper

Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance cameras.

Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Table Of Contents Introduction ........................................................................................ 4 The function of the lens ............................................................... 5 Sensor Format.................................................................................... 5 The Iris (Diaphragm)..................................................................... 6 Focal Length ........................................................................................ 8 Field of View........................................................................................ 8 Magnification .................................................................................... 14 Optical Speed: f-number ............................................................ 14 Depth of Field ................................................................................... 15 Calculating the depth of Field................................................. 16 Milestone System ........................................................................... 21

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Introduction Today there is no technical reason why the image on an IP camera should not be top quality. If there are problems with the image, it is more than likely down to the lens not being the right one for the job. Selecting the right lens for the application is one of the most important tasks in designing a surveillance solution. This article covers a step by step process to “do the math” for lenses to help you select the best lens so that your customer sees the best quality images, and provide them with the documentation to support your choice. To select the best lens you need to take several factors into account: • • • • • • • •

Type of lens Amount of light required on the camera sensor Format of the sensor Focal length of the lens (FL) Field of view (FOV) Magnification (M) f-number (f) Depth of field (DOF)

There are many different types of lenses used for video surveillance applications, probably the most common is a fixed focal length (FFL) video lens. This typically fitted with an automatic iris that optimizes the amount of light that reaches the sensor to give the best quality image. To cover a range of applications and fields of view (FOV) lenses are available in: • • •

Wide-angle (90°) Medium-angle (40°) Narrow-angle (5°)

To cover a wide scene and have the ability to get a close-up with the same camera you would use a variable FOV, vari-focal or zoom lens. Using a vari-focal lens you can fine tune the focal length (FL) of the lens for a specific application. A Pan/Tilt mechanism further increases the camera’s FOV by allowing you to move the camera to view different scenes, a camera with all three functions, pan, tilt and zoom is typically called a PTZ camera. Author:

Eric Fullerton, Chief Sales and Marketing Officer, Milestone Systems, the world’s leading innovator and thought leader of open platform IP video management software.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

The function of the lens A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element. A compound lens is made up of an array of simple lenses (elements) with a common axis. By using multiple elements allows the lens manufacturer to correct more optical aberrations than is possible with a single element. Manufactured lenses are typically made of glass or transparent plastic. The lens in a surveillance camera focuses an image of the scene onto the camera sensor. Camera sensors come in a variety of formats and the correct lens must be used to get the best results from each format.

Sensor Format In IP surveillance cameras, the sensor format is the shape and size of the image sensor. The sensor format determines the angle of view of a particular lens when used with a particular camera. Larger image sensors capture images with less noise and greater dynamic range than smaller sensors. Both the signal-to-noise ratio and sensor unity gain are proportional to the square root of image sensor area. The EIA and NTSC standards define that all surveillance sensor formats have a horizontal by vertical geometrical ratio of 4 x 3. There are three popular sensor formats that you will find in surveillance cameras: ¼”, 1/3” and ½”.

Figure 1: Sensor Format

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

The sizes (labels) used to reference the type of sensor format do not correspond directly to the actual size of the sensor, in each case the actual dimensions of the sensor are a little smaller. These labels are derived from the original Videcon television tube used in early TV cameras that had a 1” diameter tube with an actual scanned area (active sensor area) of about 16mm in diameter.

Figure 2: Videcon Television Tube The early labels for the sensor sizes have stuck with the industry. The actual dimensions for use in calculations of each sensor format are given in the table below:

Any lens designed for a larger sensor format can be used with a smaller sensor format, but the opposite is not true. For example, a lens designed for a 1/3” sensor will not work correctly on a ½” sensor format, it will produce vignetting, a dark area surrounding the image.

The Iris (Diaphragm) Behind the lens there is an iris or diaphragm. An iris is a thin opaque structure with an opening (aperture) at its centre. The size of the aperture regulates the amount of light that passes through the lens to the sensor. The centre of the iris aperture coincides with the optical axis of the lens system.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Figure 3: A Six-Blade Iris The iris consists of a series of overlapping metal leaves that open and close to control the amount of light that reaches the sensor. A video camera lens has a mechanical iris function in which a motor automatically opens and closes the iris aperture to optimize the image from the camera. The iris motor is controlled by the video signal output from the sensor.

Figure 4: Iris Aperture Positions

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Focal Length The focal length (FL) of a lens is a measure of how strongly it converges (focuses) or diverges (diffuses) light. This is known as optical power and a lens with a short focal length has greater optical power than one with a long focal length.

Figure 1: The focal point (F) and focal length (FL) of a positive (convex) lens and a negative (concave) lens For a thin lens in air, the focal length is the distance from the center of the lens to the principal focal point of the lens. In a surveillance camera the surface of the image sensor is placed at the focal point of the lens. For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam of parallel light will be focused to a single spot. For a diverging lens (for example a concave lens), the focal length is negative, and is the distance to the point from which a parallel beam appears to be diverging after passing through the lens.

Field of View In surveillance, the field of view (FOV) is that part of the scene that is visible through the camera at a particular position and orientation in space. Objects outside the FOV are not recorded, this becomes important when gathering evidence. Although related, FOV is not exactly the same as angle of view (AOV). FOV is measured in linear dimensions (feet, inches, meters, etc.), AOV (more properly called the angular field of view) is measured in (dimensionless) degrees of arc. FOV increases with distance, AOV does not. FOV changes as the camera rotates, AOV does not. So, while AOV is useful for lens design, FOV is more useful for you in designing a surveillance solution. Calculating the field of view helps you select the appropriate camera (sensor format) and lens for a surveillance task. Note that while commercial video lenses are constructed from multiple elements, the simple lens shown in the diagram has the same effective focal length.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Using simple geometry the scene size seen by the sensor is inversely proportional to the lens focal length (FL). The diagram shows the projected image on the sensor (h) of the scene (H) at some distance D. Using similar triangles we can calculate the vertical angle of view H and then vertical angle of view θh.

Figure 2: Side View for Vertical Field of View (FOV) Calculation

The vertical AOV θh is then calculated using trigonometry.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

For the horizontal FOV:

Figure 3: Plan View for Horizontal Field of View (FOV) Calculation The horizontal AOV θw is then calculated using trigonometry.

Refer to the FOV tables for the AOV and scene sizes for lenses of different focal length and distance to scene.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Field of view and scene sizes for ¼” sensor format

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Field of view and scene sizes for 1/3” sensor format

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Field of view and scene sizes for ½” sensor format

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Magnification Optical magnification is the ratio between the apparent size of an object (or its size in an image) and its true size. For surveillance applications the overall magnification of a specific camera lens and monitor size depends on: • • •

Lens focal length FL Sensor format Monitor size

Because surveillance cameras have a fixed size of sensor the camera can only see as much of the image as will fit on its sensor. The magnification at the camera Ms is related to the focal length FL and the diagonal of the sensor d:

When the image is displayed on a monitor it is magnified again. The magnification at the monitor Mm is related to the monitor diagonal dm and the sensor diagonal ds:

The combined magnification of the lens and the monitor is then:

Optical Speed: f-number The f-number (sometimes called focal ratio, f-ratio, or relative aperture) of a lens is the focal length (FL) divided by the "effective" aperture diameter (d). It is a measure of how much light the lens collects and transmits to the sensor. It is also called the lens speed or optical speed.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

As the focal length of a lens increases the aperture diameter must increase proportionately to keep the f-number the same. The same relationship applies to the amount of light transmitted to the sensor, for example, an f/2.0 lens transmits four times as much light as an f/4.0 lens with the same focal length.

Figure 4: Decreasing apertures, increasing f-numbers The diagram shows decreasing apertures, that is, increasing fnumbers, in one-stop increments. Each aperture transmits half the light to the sensor as the previous one. The actual size of the aperture will depend on the focal length of the lens. The more light the lens can collect and transmit to the sensor, the better the contrast and image quality will be. A large lens collects more light and therefore permits the camera to operate in lower light levels. Most lenses have an iris ring marked with f-numbers such as 1.4, 2.0, 2.8, 4.0, 5.6, 8.0, 11, 16, 22, C. The difference between each stop is a factor of 2 in the light transmitted by the lens. Changing the f-number from f/2.0 to f/1.4 doubles the amount of light transmitted to the sensor by the lens. C indicates that the iris is closed and no light is transmitted.

Depth of Field The depth of field (DOF) is the portion of a scene that appears sharp in the image on the sensor. Although a lens can precisely focus at only one distance, the focused distance, the decrease in sharpness is gradual on either side of the focused distance, so that within the DOF, you see the image as in focus under normal viewing conditions.

Figure 5: A view with a shallow depth of field

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

The DOF is determined by the focused distance (the distance to the plane that is perfectly in focus), the focal length, and the f-number.

Calculating the depth of Field To calculate the depth of field at a specific focus distance we first need to know two characteristics for the sensor and the lens: • •

The circle of confusion for the sensor The hyperfocal distance for the lens

Circle of Confusion: with any lens a precise focus is possible at only one distance, the focus distance. At the focus distance, a point object will produce a point image. At any other distance, a point object is defocused, and will produce a blur spot shaped like the aperture (circular). When this blur spot is sufficiently small, it is indistinguishable from a point, and appears to the eye to be in focus, we say it is “acceptably sharp”. The diameter of the blur spot increases with distance from the point of focus and the largest diameter blur spot that is indistinguishable from a point (seen by the eye as focused) is known as the circle of confusion. The diameter of the blur spot increases gradually so the limits of depth of field are not hard boundaries between sharp and unsharp. The area of the scene within the depth of field appears sharp (to the eye) and the areas in front of and beyond the depth of field appear blurred. We can use the Zeiss formula to calculate the circle of confusion (c):

where d is the diagonal of the sensor. The table below shows the value of c for the common sensor formats used in surveillance cameras.

Hyperfocal distance: is the nearest focus distance at which the DOF extends to infinity. Focusing the camera at the hyperfocal distance results in the largest possible depth of field for a given f-number. Focusing beyond the hyperfocal distance does not increase the far DOF (which already extends to infinity), but it does decrease the near DOF in front of the subject, so overall this would decreas the total DOF.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

The hyperfocal distance H is given by:

Where FL is the focal length of the lens, f is the f-number, and c is the circle of confusion for the sensor format. Calculating the depth of field: when the camera is focused on a subject at distance s, where s is large in comparison with the focal length of the lens, the distance from the camera to the near limit of the DOF Dn and the distance from the camera to the far limit of the DOF Df are: the near limit

the far limit

The depth of field Df − Dn is:

For the case when s is the hyperfocal distance,

and

As you can see for s ≥ H, the far limit of the DOF is at infinity and the DOF is infinite and in this case only objects at or beyond the near limit Dn of the DOF will appear with acceptable sharpness. Substituting for H and rearranging, the DOF can be expressed as:

On the following pages, we provide some depth of field tables.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Milestone System Innovator. Milestone Systems is internationally recognized as an innovator and thought leader in open platform IP video management software. Milestone’s XProtect products operate as the core of surveillance systems: connecting, sharing and managing all devices through a single interface that is easy to learn and operate. Easy to use. The XProtect platform is easy to use, proven in operation and scales to support unlimited devices. XProtect products support the widest choice of network video hardware and are designed with an Application Programming Interface (API) that integrates seamlessly with other manufacturers’ systems. Best-of-breed. Using XProtect, you can build scalable, “best of breed” solutions to reduce cost, optimize processes, protect assets and ultimately increase value in a company’s products and services.

© Copyright Milestone Systems 2009

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Milestone White Paper Lens Calculations – Do the Math A step-by-step guide to lens parameters and calculations for video surveillance.

Milestone Systems is the industry leader in developing true open platform IP video management software. The XProtect™ platform gives users a powerful surveillance solution that is easy to manage, reliable and proven in more than 50,000 customer installations worldwide. With support for the industry’s widest choice in network hardware and integration with other systems, XProtect provides best-of-breed solutions to “video enable” organizations – reducing costs, optimizing processes, and protecting assets. Milestone software is sold through authorized partners in over 90 countries. Office Locations: Milestone Systems Inc. 8905 SW Nimbus Avenue, Beaverton, OR 97008, United States Tel: +1 (503) 350 11000 Milestone Systems A/S (Headquarters) Banemarksvej 50, 2605 Brøndby, Denmark Tel: +45 88 300 300 Milestone Systems DE Am Kleefeld 6a, D-83527 Haag i.OB., Germany Tel: +49 (0) 8072 442173 Milestone Systems Italy Via Paisiello,110, 20092 Cinisello Balsamo, Milano, Italy Tel: +39 02 6179 508 Milestone Systems UK, Ltd. 118 Codnor Gate, Ripley, Derbyshire DE5 9QW, Great Britain Tel: +44 (0) 1773 570 709 Milestone Systems France 121 rue d'Aguesseau, 92100 Boulogne-Billancourt, France Tel: +33 141 03 14 82 Milestone Systems Japan c/o Royal Danish Embassy, 29-6, Sarugaku-cho, Shibuya-ku, Tokyo 150-0033, Japan Tel: +81 (0)3 3780 8749 Milestone Systems Pte. Ltd. 30 Robinson Road, 13-03 Robinson towers, Singapore 048456 Tel: +65 6225 2686 Milestone Systems Middle East P.O, Box 500809, DIC, Building 5 IEB, 6th floor Office 606, Dubai, United Arab Emirates Tel: +971 50 8827093 Corporate website: www.milestonesys.com

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