Effectivefocal lengthformula

The lab of Aristide Dogariu of University of Central Florida is investigating non-line-of-sight imaging utilizing the spatial coherence of light hitting a wall instead of laser light scattered off of that wall and the target behind it.3 This could lead to modeling of the hidden target without requiring ultrafast laser illumination, making real-world applications of the technology more portable and easy to use.

The light scattering directly off of the wall is much stronger than the secondary scatter of light off of the indirect object, but there is a time delay between them that allows highly sensitive detectors with a high enough temporal resolution to differentiate the two signals.2

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Edmund Optics® (EO) designs and manufactures imaging lenses and ultrafast laser optics, which are both used in non-line-of-sight imaging systems.

Allow cars to sense approaching vehicles or pedestrians around corners before they are in the car’s direct line of sight2

The thin lens equation calculator will help you to analyze the optical properties of the simple lens. Keep reading to learn about the thin lens equation and understand how a lens can magnify the image of an object. Everything is about light, so be sure to check out the principles of light refraction too!

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The software first stores all measurements in a 3D spatial-temporal volume. It then resamples measurements along the time axis, convolves the result with an inverse filter in the frequency domain, and resampling result along depth axis to recover the hidden object.2

Let law enforcement, firefighters, and emergency medical services detect presence of people in dangerous situations from a safe distance2

Taking this emerging technology and creating a practical solution for real-world use that is portable and not dangerous to observer’s eyes is extremely challenging. One of the main issues with non-line-of-sight imaging is the limited amount of light that makes its way back to the detector, which must be able to pick up this very small amount of light and differentiate it for any ambient light sources. The return signal to the detector is the result of two consecutive scattering events, leading to an extremely high loss. Return signals can be as low as one photon per laser pulse.1

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We encourage you to check similar cases for the diverging lens, which has a negative focal length f < 0 with our calculator!

Let us consider five different situations for a converging lens (f > 0). You can check it with our thin lens equation calculator!

However, the Stanford Computational Imaging Lab has developed a non-line-of-sight imaging system that works outdoors under indirect sunlight.2 They successfully imaged an object made out of retroreflective tape that was obscured by a wall, which bodes well for the future of this technology.

If we place the object near the lens, we will get its image somewhere. The position, orientation, and size of this image depend on two things: the focal length of the lens (which is specific for the particular lens) and the position of the original object. We can predict what we will see with the following thin lens equation:

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The magnification of a lens is the ratio of the size of the image to the size of the object. Hence, to find the magnification of a lens, take the ratio of the two. You can also calculate magnification by taking the ratio of the image-lens distance to the object-lens distance.

Highly sensitive cameras such as single-photon avalanche photodiode array cameras are needed to measure the propagation of picosecond and femtosecond pulses of light in real time. The detector receives two different return signals: an initial signal of light scattered directly off of the wall and a secondary signal of light scattered off of the target, which is the signal used for non-line-of-sight imaging. This time-of-flight information is then used to reconstruct a series of ellipsoids that all overlap at a given point on the hidden target, allowing computational software to calculate the distance between the camera and the hidden target and recreate a 3D model of the target.

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Technical information and application examples including theoretical explanations, equations, graphical illustrations, and much more.

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A direct line of sight between an object and a camera or detector is typically needed for every imaging application except for extreme cases such as light bending due to gravitational lensing in astronomy. But for the most part, imaging applications are limited to light propagating in a straight line. However, that is starting to change as some cutting edge research is opening up possibilities to image around corners and around obstacles. A combination of lasers, sensitive cameras, and computational reconstruction methods can be used to detect objects hidden by obstacles by scattering light off of surrounding objects.

You can compute the magnification of the created image, too (see the mirror equation calculator). It can be easily estimated if we know the distance of object x and the distance of image y:

The process for non-line-of-sight imaging is similar to that of LiDAR (light detection and ranging), where a laser pulse is sent towards an object and the time-of-flight of the light scattering back off of the object is used to measure the distance between the object and a detector. However, non-line-of-sight imaging images objects obscured by obstacles by adding another scattering event to this process.1

Remember that magnification must always be a positive number. That's why we have taken the absolute value of y, which generally may be both positive and negative.

More development is still needed before non-line-of-sight imaging technology becomes available in practical commercial systems, but it is a promising solution for the next generation of imaging applications.

The power (P) of a lens is the reciprocal of its focal length (f). Hence we can express the formula for the power of a lens as:

There are two basic types of lenses. We can distinguish converging lenses, which have focal length f > 0, and diverging lenses for which focal length f < 0. It should also be noted that when the image distance is positive y > 0, then the image appears on the other side of the lens, and we call it a real image. On the other hand, when y < 0, then the image appears on the same side of the lens as the object, and we call it a virtual image.

A 3D object can be broken down into a collection of many individual points that scatter light. The summation of all of these points can reconstruct a model of the original object. If the detector can distinguish return pulses with a temporal resolution of 100ps, this corresponds to a spatial resolution of points on the hidden target of approximately 1.5cm. 1

No, the thin lens formula is not different for different lenses. The thin lens formula is the same for both convex and concave lenses.