Projector Pattern - pattern projector

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Camera Size comparison with lens

Spin-component scaled (SCS-)MP2 calculations can be performed analogously to DF-MP2 calculations using the classes SCSDFRMP2 and SCSDFUMP2, which also have got aliases such as SCSMP2 inside the respective modules. The default scaling factors can be changed to arbitrary values:

The module-level mp.MP2(mf) constructor can infer the correct method based on the level of symmetry-breaking in the mean-field argument. For more explicit control or inspection, the respective classes and functions can be found in mp2.py (restricted), ump2.py (unrestricted), and gmp2.py (general).

As a general guideline, focal lengths below 35mm are considered wide-angle, around 50mm is a standard lens, and above 75mm is telephoto.

Please note that this part of the documentation does not describe the older mp.dfmp2.DFMP2 implementation, which is still returned by the density_fit() method of the mp.mp2.MP2 class; instead it is about the newer DFRMP2 and DFUMP2 classes, which need to be imported directly from mp.dfmp2_native or mp.dfump2_native at present.

70-180mm F/2.8 Di III VC VXD G2 (Model A065) has evolved to G2 level.This is the world’s smallest and lightest, fast-aperture telephoto zoom lens for Sony E-mount with astounding portability and superb image quality.

Most camera lenses clearly display the focal length value. For example, in a lens labelled "28-75mm F/2.8", the "xx mm" part denotes the focal length range. There are two main types of lenses in this regard - prime lenses with a fixed focal length shown as a single number like "20mm", and zoom lenses which have a variable focal length range like "28-75mm". So if you see a focal length specified as a range of numbers, that indicates it's a zoom lens capable of varying its focal length. But if only one focal length number is listed, it's a prime lens with a single, fixed focal length.

For technical reasons (incompatible algorithms), the “native” DF-MP2 implementation is not implemented as a subclass of mp.mp2.MP2, but it is written as an independent class instead. Currently, the classes DFRMP2 (for RHF references) and DFUMP2 (for UHF references) need to be imported from the respective modules mp.dfmp2_native and mp.dfump2_native:

set_frozen() will freeze the core orbitals determined by sum of the core electrons of atoms, which are shown as follows. The current rule is the same as that of ORCA program.

28-75mm F/2.8 Di III VXD G2 (Model A063) is the second-generation fast-aperture standard zoom lens for Sony and Nikon full-frame mirrorless cameras, offering significantly improved optical and autofocus performance and new function customization. You can find 28-75mm complete review online.

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The relaxed density should be used to calculate properties if the MP2 method is well-behaved for the system in question. Properties calculated thereby correspond to the correct derivative of the MP2 energy with respect to an appropriate external perturbation. This is illustrated in examples/mp/11-dfmp2-density.py, where the dipole moment of chloromethane is calculated much more accurately with the relaxed density than with the unrelaxed one. To calculate the relaxed density, a set of CP-SCF type equations needs to be solved in one of the steps. In ill-behaved systems, for example if there is multi-reference character, the MP2 natural occupation numbers can be substantially larger than two or smaller than zero.

MP2 can be combined to great benefit with density fitting (DF), also known as the resolution of the identity (RI) approximation. While the formal scaling remains \(O(N^5)\), the prefactor and the overall computational cost are reduced strongly, so that calculations can be performed on much larger molecules than with conventional MP2. Provided that a suitable auxiliary basis set is used, the resulting DF/RI errors in reaction energies, geometries, properties etc. are negligible compared to the intrinsic errors of MP2.

Photographers should select Portrait lens based on their desired angle of view, subject magnification needs, and aperture requirements for different shooting scenarios like landscapes, portraits, sports, and wildlife.

The MP2 module in PySCF supports a number of reference wavefunctions with broken spin symmetry. In particular, MP2 can be performed with a spin-restricted, spin-unrestricted, and general (spin-mixed) Hartree-Fock solution, leading to the RMP2, UMP2, and GMP2 methods.

Changing the focal length drastically alters the perspective and composition. For example, a portrait taken at 35mm with the TAMRON 35-150mm F/2-2.8 lens shows the subject in an environmental context with the background. But at 150mm, the longer telephoto focal length compresses the perspective, magnifying the subject's face while blurring the background for a shallow depth of field effect. This ability to creatively adjust the angle of view by varying the focal length of a zoom lens allows you to capture vastly different looks and impressions.

F stopsexplained

By default, MP2 calculations in PySCF correlate all electrons in all available orbitals. To freeze the lowest-energy core orbitals, use the frozen keyword argument:

For example, a APS-C lens at 20mm focal length has an equivalent full-frame angle of view of around 30mm (20 x 1.5). Consulting crop factor charts helps visualize the angles of view for different focal lengths on APS-C sensors when choosing lenses.

Lenses with shorter focal lengths and wider maximum apertures tend to produce greater depth of field. Wide-angle lenses are excellent digital photography lenses, where you want to capture both foreground and background elements in crisp focus. Their short focal length increases depth of field, allowing details throughout the scene to be rendered sharply.

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In RHF-DF-MP2 calculations, orbitals can be frozen by specifying either an integer, or a list. Frozen core UHF-DF-MP2 calculations are initiated by providing either an integer, or two lists of equal length (for the alpha and beta orbitals):

The 17-70mm F/2.8 Di III-A VC RXD (Model B070) is a large-aperture standard zoom lens for APS-C format mirrorless cameras. With a focal length range of 17mm to 70mm (a full-frame equivalent of 25.5-105mm) for daily use, this achieves a 4.1x zoom. The optical design ensures high resolution and high contrast not just in the center of the image but also in corners and at the edges. The quiet AF drive motor and the VC image stabilization mechanism facilitate hand-held shooting. In addition, by counteracting focus breathing, the 17-70mm F2.8 empowers users' expression of their creative intentions to the fullest degree. This highly practical lens allows you to easily enjoy the high image quality of a large F2.8 aperture for both still and video shooting.

The 50-400mm F/4.5-6.3 Di III VC VXD (Model A067) is an ultra-telephoto zoom lens with an 8x zoom starting at 50mm at the wide-angle end and compatible with full-frame mirrorless cameras. The lens delivers uncompromised high image quality over the entire 50-400mm focal length range, yet is as compact and lightweight as a 100-400mm class lens. Equipped with the VXD mechanism and the VC mechanism, the lens can quickly focus on the subject's movement when shooting sports and wild birds. The 50-400mm F4.5-6.3 is a new ultra-telephoto zoom lens that combines unparalleled image quality and mobility.

The 17-50mm F/4 Di III VXD (Model A068)It's the world’s first lens covering from ultra wide-angle 17mm to the standard 50mm focal length. The highly-compact TAMRON 17-50mm F/4 Di III VXD (model a068) for Sony E-mount full-frame mirrorless cameras offers maximum versatility for still and video creators. From landscapes to living rooms, this lens captures all that you see.

The maximum aperture f-number is calculated by dividing the focal length by the effective aperture diameter. So a lens with a lower maximum f-number like f/2.8 has a wider maximum aperture compared to one with a higher number like f/5.6.

The 150-500mm F/5-6.7 Di III VC VXD (Model A057) is compact enough to be handheld while maintaining a focal length of 500mm on the telephoto end. It allows users to easily enjoy the world of the 500mm ultra-telephoto lens while maintaining its high image quality. The high-speed, high-precision AF with excellent tracking performance and the VC mechanism support handheld shooting in the ultra-telephoto range.

Telephoto zoom lenses magnify distant subjects, making them the best lens for wildlife photography. Their long reach also flattens perspective when shooting landscapes during hiking trips. However, telephoto zooms also excel for portraits. Their shallower depth of field produces beautiful blurred backgrounds that isolate the subject with smooth bokeh. This compression effect renders flattering features and makes subjects pop against the defocused setting for striking portraits.

Focus distance

Wide-angle lenses span from ultra-wide to standard focal lengths. The ultra-wide capability lets you get up close to large subjects like buildings while still capturing an immense view, resulting in dynamic, sweeping shots. The exaggerated perspective also enables unique portraits and pet photos that emphasize the subject's size and surroundings creatively.

Lenses are broadly categorized into three types based on their angle of view: wide-angle, standard, and telephoto. A standard lens provides an angle of view similar to the human eye's natural field of vision. Wide-angle lenses offer an expansive wide angle of view, while telephoto lenses have a narrow, magnified angle ideal for distant subjects.

There is also an older variant of DF-MP2 implemented in mp.dfmp2, which does not exploit the advantages of density fitting fully, and may therefore have much higher memory demands for larger molecules. Please note that the density_fit() method of the conventional mp.mp2.MP2 class provides an instance of the old implementation, not the new one! Currently, the “native” implementation can only be used by importing it from mp.dfmp2_native or mp.dfump2_native directly as shown above.

Example of a zoom lens: 28-75mm F/2.8 Di III VXD G2 (Model A063) Example of a prime lens: 20mm F/2.8 Di III OSD M1:2 (Model F050)

A typical use case for the unrelaxed density is to calculate starting orbitals for a CASSCF calculation, which can be used despite the system being described poorly at MP2 level otherwise. In contrast to the relaxed density, the natural occupation numbers of the unrelaxed density are always between two and zero. examples/mp/12-dfump2-natorbs.py shows how to calculate natural orbitals for the allyl radical, which has a significantly spin-contaminated UHF wave function. On the other hand, the unrelaxed density will often give very poor results for properties (such as electrostatic moments).

When using an APS-C sensor, you'll need to calculate the "35mm equivalent" focal length to understand the actual angle of view, as focal lengths are traditionally referenced to the full-frame format. This is done by multiplying the APS-C lens' focal length by the crop factor (around 1.5x for most brands).

The 35-150mm F/2-2.8 Di III VXD (Model A058) is a high-resolution travel zoom lens that covers everything from the 35mm wide angle to the 150mm telephoto focal length, the first zoom lens achieving an aperture of F2 at the wide-angle end. It has a groundbreaking fast-aperture and utilizes the linear motor focus mechanism VXD (Voice-coil eXtreme-torque Drive), thereby achieving high speed, high precision autofocusing. The innovative lens design enabled us to greatly improve the lens's grip and functionality. The software, developed in-house, enables to easily customize functions and to update firmware.

Relaxed and unrelaxed 1-RDMs can be calculated for the RHF and UHF variants of the “native” DF-MP2 implementation. The points below provide some advice on choosing the correct type of MP2 density.

Lenses with wider maximum apertures (smaller f-numbers) are more light-sensitive, enabling faster shutter speeds to freeze action and better low-light performance. They also provide a shallower depth of field for separating subjects with beautiful background blur.

Focal length

So when evaluating lenses, consider both the focal length for your desired angle of view and perspective, as well as the maximum aperture f-number for its low-light capabilities and creative control over depth of field. Both specifications play vital roles in determining the lens' overall imaging performance.

Second-order Møller–Plesset perturbation theory (MP2) [26] is a post-Hartree–Fock method. MP2 calculations can be performed in PySCF with or without density fitting, depending on the initial SCF calculation.

Focaldistance vsfocal length

When light rays travel through a lens, they bend (refract) and converge at a specific point called the focal point. This is where the light focuses and forms an image. The focal length refers to the distance between the optical center of the lens and the image sensor. At this precise length from the lens, the sensor captures the focused image formed by the converging light rays.

A full-frame sensor measures 36mm x 24mm, which is the same size as 35mm film. This larger sensor captures a wider field of view, greater dynamic range, and lower noise compared to smaller sensors. The APS-C format has a smaller 23.5mm x 15.6mm* sensor size, resulting in a more tightly cropped angle of view.

Focal length refers to the distance between a lens's optical center and the camera's image sensor. This measurement critically dictates the angle of view captured. Lenses with shorter focal lengths are classified as wide-angle, providing an expansive field of view. Conversely, those with longer focal lengths are telephoto lenses, offering a narrower, magnified perspective. Standard lenses fall in between these two extremes. When selecting optics, carefully consider the focal length best suited to render your desired angle of view and framing for the subjects or scenes you aim to photograph.

When using an interchangeable lens camera like a DSLR or mirrorless system, understanding focal length is crucial for capturing impressive photos. The focal length influences the angle of view, focus area, and degree of background blur (bokeh). By learning how focal length works, you can choose lenses that allow you to frame your subjects exactly as you envision - adjusting the field of view, pinpointing the focus, and controlling background defocus. Mastering this fundamental lens characteristic opens up creative possibilities for gorgeous, impactful imagery with your camera system.

11-20mm F/2.8 Di III-A RXD (Model B060) is the world's first compact, lightweight F2.8 ultra wide-angle zoom lens for e-mount Sony APS-C mirrorless cameras. Can be the Best Lenses for Filmmaking.

The 20-40mm F/2.8 Di III VXD (Model A062) is a new large-aperture standard zoom lens that thoroughly pursues portability. While covering the range from the ultra-wide angle of 20mm to the standard range of 40mm, it is the smallest and lightest in its class. It also offers high image quality throughout the entire zoom range, making it useful not only for still image shooting but also for video recording such as vlogging. The VXD, which is quiet and agile, achieves high-speed, high-precision autofocusing. It is a new, unprecedented large-aperture standard zoom lens that allows users to easily enjoy taking out and shooting both still and video.

The key point about focal length is that it directly determines the angle of view captured by the lens. The angle of view refers to the width of the scene that the camera can capture through the lens - the larger the angle, the wider the field of view.

Ultra-telephoto zoom lenses provide an extreme magnification capability that allows you to enlarge and capture distant subjects that are impossible to get physically close to. This makes them perfectly suited for photographing wildlife from a safe distance, as well as action at large sporting venues, aircraft, trains and other far-away moving objects

On the flip side, telephoto lenses with longer focal lengths exhibit a very shallow depth of field. This results in pleasantly blurred bokeh backgrounds that make the main subject really stand out against the soft defocused areas. Leveraging this compressed look with pronounced bokeh is ideal for portraits and other scenes where you want to isolate the subject from the background.

Focal lengthcamera

A standard best zoom lens offers a versatile focal range spanning from wide-angle to telephoto perspectives around the 50mm mark. These flexible lenses excel not just for candids and portraits, but prove invaluable across a diverse array of shooting situations. At the wide end, they can capture expansive landscapes, while the telephoto capabilities allow zooming in on distant subjects like animals or architectural details. With this walkaround range, a quality standard zoom is an extremely versatile option capable of handling everything from environmental shots to telephoto compression effects in a single lens.

A lower f-number indicates a wider maximum aperture diameter, allowing more light to pass through the lens onto the sensor. This greater light gathering capability provides several advantages.

Note also the existence of a native DF-MP2 implementation, which does not depend on the integral approximation in SCF, and which is significantly faster than the default implementation of MP2 with density fitting.

To freeze occupied and/or unoccupied orbitals with finer control, a list of 0-based orbital indices can be provided as the frozen keyword argument:

Both modules also make the respective classes available under the alias DFMP2. The file examples/mp/10-dfmp2.py contains a simple example for a DF-MP2 energy calculation.

Unless specified by the user, an appropriate auxiliary basis set is determined automatically. Note that there exist different auxiliary basis sets for Coulomb and exchange fitting in DF-HF on the one hand, and for correlation fitting in MP2 or other dynamic correlation methods on the other hand. The DF approximation in MP2 does not depend on the approximation taken for SCF. Arbitrary auxiliary sets can be specified with the auxbasis option:

The 17-28mm F/2.8 Di III RXD (Model A046) achieves a filter diameter of ø67mm, which is surprising for a large aperture ultra wide-angle zoom lens for full-frame cameras. It’s small and light weight with a good camera balance. It's a dedicated lens for mirrorless interchangeable -lens cameras that can be carried easily and can be used in various situations.

Since lenses are designed for a specific sensor size, you'll need to select one that matches your camera's sensor format. Full-frame lenses can be used on APS-C bodies but provide a further crop. However, APS-C lenses cannot fully cover a full-frame sensor.

While focal length is critically important, another key factor to consider when choosing a lens is the image sensor size of your camera body. Digital cameras primarily use two main sensor formats - 35mm full-frame and APS-C crop sensors.

Product Page | 11-20mm F/2.8 Di III-A RXD (Model B060) is the world's first compact, lightweight F2.8 ultra wide-angle zoom lens for Sony E-mount APS-C mirrorless cameras. Can be a great choice for video shooting.

The 70-300mm F/4.5-6.3 Di III RXD (Model A047) for full-frame Mirrorless lenses is a telephoto zoom lens designed and created so photographers of all skill levels can enjoy high quality images comfortably. The 70-300mm F4.5-6.3 covers a broad telephoto zoom range yet is the small and lightest weight. With special emphasis on resolving power, TAMRON has deployed special lens elements appropriately arranged to correct chromatic aberration, generally very strong in a telephoto lens, as well as other aberrations. Users can enjoy high-resolution images combined with stunning bokeh qualities that are achievable only with a telephoto lens. The lens also incorporates the RXD, a high-speed precision AF drive system that is remarkably quiet. The 70-300mm F4.5-6.3 is a versatile lens for photographing landscapes, sports and other action, pets, wildlife, and more. The lens also demonstrates its potential for portrait shooting, casual snapshots, and scenarios that require you to be mobile and shoot handheld, like sporting events.

Another key attribute related to focal length is depth of field. Depth of field refers to the zone of acceptable sharpness in an image, extending from the focused subject to the background. A deep depth of field means that both the subject and background appear in focus over a wide range. Conversely, a shallow depth of field renders a blurred, smooth bokeh effect in the out-of-focus background areas surrounding the subject.

This implementation can calculate energies, as well as unrelaxed and relaxed one-particle density matrices. Analytical gradients are not available yet. RHF and UHF references are supported throughout.