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64-669: The observatory was founded in October 1971 as a collaboration between Tel Aviv University and the Smithsonian Institution , and named after the late Dr. George S. Wise , the first President of the Tel Aviv University. The observatory is a research laboratory of Tel Aviv University. It belongs to the Raymond and Beverly Sackler Faculty of Exact Sciences and it serves mainly staff and graduate students from

128-463: A field of view almost one-degree wide on one of the CCDs (a SITe 2048x4096 pixel array) at the cost of slightly larger than optimal PSF sampling and some edge-of-field distortions. However, this instrument never produced satisfactory images and its use was discontinued. A new CCD camera entered regular use in 2006: it is a Princeton Instruments Versarray with 1340×1300 pixels each 20  μm wide, with

192-556: A peak quantum efficiency of 95% and good response in the blue part of the spectrum. Another camera was operated from the end of 2007 to about 2014; this is a CCD mosaic covering a one-degree non-contiguous field of view at f/7 in a single exposure (the LAIWO (Large Array Imager of the Wise Observatory) camera). This camera is composed of four 4096x4096 pixel non-butted Fairchild CCDs that are thick and front-illuminated, thus have

256-403: A perfect point source object is central to the idea of PSF. However, there is no such thing in nature as a perfect mathematical point source radiator; the concept is completely non-physical and is rather a mathematical construct used to model and understand optical imaging systems. The utility of the point source concept comes from the fact that a point source in the 2D object plane can only radiate

320-472: A perfect uniform-amplitude, spherical wave — a wave having perfectly spherical, outward travelling phase fronts with uniform intensity everywhere on the spheres (see Huygens–Fresnel principle ). Such a source of uniform spherical waves is shown in the figure below. We also note that a perfect point source radiator will not only radiate a uniform spectrum of propagating plane waves, but a uniform spectrum of exponentially decaying ( evanescent ) waves as well, and it

384-878: A plan to establish an NYU Study Abroad Campus in Israel based at Tel Aviv University. In 2024 QS World University Rankings ranked Tel Aviv University 214th in the world, making it the highest ranked university in Israel. In 2016, its subject rankings were: 202nd in Arts and Humanities, 295th in Engineering and Technology, 193rd in Life Sciences and Medicine, 208th in Natural Science, and 240th in Social Sciences and Management. The Center for World University Rankings ranked Tel Aviv University 81st in

448-419: A point source which is produced by a convergent (uniform) spherical wave whose half angle is greater than the edge angle of the lens. Due to intrinsic limited resolution of the imaging systems, measured PSFs are not free of uncertainty. In imaging, it is desired to suppress the side-lobes of the imaging beam by apodization techniques. In the case of transmission imaging systems with Gaussian beam distribution,

512-600: A response peaking in the red with approximately 42% quantum efficiency. A smaller CCD with very high quantum efficiency and fast readout, centered between the four large CCDs, is used for guiding and fast photometry of selected objects. LAIWO was a cooperative endeavour of the Wise Observatory (PI: T. Mazeh) with the Max Planck Institute for Astronomy Heidelberg (PI: T. Henning). A 46 centimeters (18 inches) prime-focus computer-controlled telescope

576-531: A spatial impulse response function . In functional terms, it is the spatial domain version (i.e., the inverse Fourier transform) of the optical transfer function (OTF) of an imaging system . It is a useful concept in Fourier optics , astronomical imaging , medical imaging , electron microscopy and other imaging techniques such as 3D microscopy (like in confocal laser scanning microscopy ) and fluorescence microscopy . The degree of spreading (blurring) in

640-638: A study center at the Mediterranean Sea , where students will undertake advanced studies of issues impacting the coastal environment and its resources. In Germany, Tel Aviv University cooperates with the Goethe-University in Frankfurt/Main. Both cities are linked by a long-lasting partnership agreement. Notable faculty members (past and present) include: Sackler Family Tel Aviv University has long held significant ties to

704-554: Is in routine robotic operation. A 50 centimeters (20 inches) wide-field telescope has been installed in 2016 and is being commissioned. This telescope is a node of the Korean OWL-Net (Optical Wide-field patroL Network) that acquires and maintains orbital information of LEO satellites by purely optical means. OWL-Net is part of and is operated by the Korea Astronomy and Space Science Institute (KASI). Observations at

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768-452: Is often found to vary with position in the image (an effect called anisoplanatism). In ground-based adaptive optics systems, the PSF is a combination of the aperture of the system with residual uncorrected atmospheric terms. The PSF is also a fundamental limit to the conventional focused imaging of a hole, with the minimum printed size being in the range of 0.6-0.7 wavelength/NA, with NA being

832-532: Is open to MBA/MSc/MA students and qualified professionals. The school offers a wide variety of courses for its visiting students in strategy, entrepreneurship, finance-accounting, marketing, organizational behavior, decisions and operations research, technology and information systems. The program also offers courses from other TAU schools on Israeli Culture, History, Economics and more. In 2013, Tel Aviv University and Ruppin Academic Center jointly created

896-500: Is put on studies of Near Earth Objects (NEOs), with the research focus being the rotational properties of NEOs and of other asteroids through the investigation of their light curves. As of 2016, the Wise Observatory is credited by the Minor Planet Center with the discovery of 17 numbered minor planets during 1999–2007. Moreover, another 8 minor planets were discovered at the Wise Observatory, but are now credited to

960-766: Is the possibility of cooperating with observatories at other longitudes for time-series studies. Such projects involve searches for stellar oscillations within the Whole Earth Telescope project, monitoring gravitational microlensing events, combined ground and space observing campaigns, etc. A project to monitor photometrically and spectroscopically Active Galactic Nuclei (AGNs) is still running, following about 30 years of data collection. Other major projects include searches for supernovae and extrasolar planets ( transiting or lensing), and investigations of star formation processes in galaxies through wide and narrow-band filter imaging. Lately, some emphasis

1024-409: Is these which are responsible for resolution finer than one wavelength (see Fourier optics ). This follows from the following Fourier transform expression for a 2D impulse function, The quadratic lens intercepts a portion of this spherical wave, and refocuses it onto a blurred point in the image plane. For a single lens , an on-axis point source in the object plane produces an Airy disc PSF in

1088-748: The Sackler family as evidenced by several schools and many endowed chairs being in their honor. As more has become known of the role of members of the Sackler family in the global opioid crisis, many including the Israel Medical Association have called for the removal of the Sackler name from the Faculty of Medicine. As of November 2021, no members of the Sackler family served on the university's board of governors. Point spread function The point spread function ( PSF ) describes

1152-1392: The Shanghai Rankings In 2022, PitchBook Data ranked Tel Aviv University 7th in the world in terms of number of alumni who have founded venture capital backed companies, the highest out of any University outside the United States. Tel Aviv University offers special programs of Jewish studies to teachers and students from the United States, France, Brazil, Argentina and Mexico. The programs are in English. The Tel Aviv University Faculty of Law has exchange agreements with 36 overseas universities, including: University of Virginia, Cornell University, Boston University, UCLA, Bucerius (Germany), EBS (Germany), McGill (Canada), Osgoode Hall (Canada), Ottawa (Canada), Queens University (Queens), Toronto (Canada), Bergen (Norway), STL (China), KoGuan (China), Tsinghua (China), Jindal Global (India), University of Hong Kong, Singapore Management University, Stockholm University (Sweden), Monash (Australia), Sydney (Australia), Sciences Po (France), Seoul (South Korea), Lucern (Switzerland), Buenos Aires (Argentina), Bocconi (Italy) and Madrid (Spain). The Coller School of Management has exchange agreements with over 100 overseas universities. The Coller Exchange Program

1216-421: The numerical aperture of the imaging system. For example, in the case of an EUV system with wavelength of 13.5 nm and NA=0.33, the minimum individual hole size that can be imaged is in the range of 25-29 nm. A phase-shift mask has 180-degree phase edges which allow finer resolution. Point spread functions have recently become a useful diagnostic tool in clinical ophthalmology . Patients are measured with

1280-429: The 1930–40s. A central role in their analysis is played by Zernike's circle polynomials that allow an efficient representation of the aberrations of any optical system with rotational symmetry. Recent analytic results have made it possible to extend Nijboer and Zernike's approach for point spread function evaluation to a large volume around the optimum focal point. This extended Nijboer-Zernike (ENZ) theory allows studying

1344-844: The Center for Technological Design in Holon , the New Academic College of Tel Aviv-Yafo , and the Afeka College of Engineering in Tel Aviv. The Wise Observatory is located in Mitzpe Ramon in the Negev desert. Faculties Independent schools Tel Aviv University has over 130 research institutes and centers. The Lowy International School (formerly known as TAU International) affords thousands of students from across

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1408-640: The Department of Astronomy and Astrophysics of the School of Physics and Astronomy, and from the Department of Geophysics and Planetary Sciences. Traditionally, the Wise Observatory Director is appointed by Tel Aviv University's Dean of Exact Sciences from the senior academic staff of the Department of Astronomy and Astrophysics. The directors of the Wise Observatory since its foundation were: The number of clear nights (zero cloudiness) at

1472-408: The PSF is modeled by the following equation: where k-factor depends on the truncation ratio and level of the irradiance, NA is numerical aperture, c is the speed of light, f is the photon frequency of the imaging beam, I r is the intensity of reference beam, a is an adjustment factor and ρ {\displaystyle \rho } is the radial position from the center of

1536-412: The PSF is shift-invariant and that there is no distortion, calculating the image plane convolution integral is a straightforward process. Mathematically, we may represent the object plane field as: i.e., as a sum over weighted impulse functions, although this is also really just stating the shifting property of 2D delta functions (discussed further below). Rewriting the object transmittance function in

1600-414: The PSF of the measuring device is very important for restoring the (original) object with deconvolution . For the case of laser beams, the PSF can be mathematically modeled using the concepts of Gaussian beams . For instance, deconvolution of the mathematically modeled PSF and the image, improves visibility of features and removes imaging noise. The point spread function may be independent of position in

1664-619: The Sackler Faculty of Medicine, there is a four year, English speaking Doctor of Medicine program which prepares students from North America for residencies in the United States and Canada. The program has a track record of excellent residency matches which far exceeds most international medical school, although as of 2022, all Israeli medical schools have been instructed to cease their programs for foreign medical students to provide more places for Israeli medical students. In May 2007, New York University and Tel Aviv University approved

1728-666: The Tel Aviv School of Law and Economics (established in 1935), the Institute of Natural Sciences (established in 1931), and the Academic Institute of Jewish Studies (established in 1954) – joined to form Tel Aviv University. Initially operated by the Tel Aviv municipality, the university was granted autonomy in 1963, and George S. Wise was its first president, from that year until 1971. The Ramat Aviv campus, covering an area of 170-acre (0.69 km ), on top of

1792-413: The Wise Observatory are allocated on a semestrial basis for the periods from the beginning of April to the end of September (first semester) and from the beginning of October to the end of March the following year (second semester). The allocation is competitive and is based on the scientific merit of each proposal. The observing time is, in principle, open to qualified observers from all over the world. Over

1856-474: The Wise Observatory site is about 170 a year. The number of useful nights, with part of the night cloud-free, is about 240. The best season, when practically no clouds are observed, is June to August, while the highest chance for clouds are in the period January to April. Winds are usually moderate, mainly from North-East and North. Storm wind velocities (greater than 40 kilometers per hour (25 miles per hour)) occur, but rarely. The wind speed tends to decrease during

1920-407: The ample supply of point sources ( stars or quasars ). The form and source of the PSF may vary widely depending on the instrument and the context in which it is used. For radio telescopes and diffraction-limited space telescopes , the dominant terms in the PSF may be inferred from the configuration of the aperture in the Fourier domain . In practice, there may be multiple terms contributed by

1984-421: The beam on the corresponding z-plane . The diffraction theory of point spread functions was first studied by Airy in the nineteenth century. He developed an expression for the point spread function amplitude and intensity of a perfect instrument, free of aberrations (the so-called Airy disc ). The theory of aberrated point spread functions close to the optimum focal plane was studied by Zernike and Nijboer in

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2048-467: The depopulated and razed Palestinian village of Sheikh Munis , was established that same year. Its succeeding presidents have been Yuval Ne'eman from 1971 to 1977, Haim Ben-Shahar from 1977 to 1983, Moshe Many from 1983 to 1991, Yoram Dinstein from 1991 to 1999, Itamar Rabinovich from 1999 to 2006, Zvi Galil from 2006 to 2009, Joseph Klafter from 2009 to 2019, and Ariel Porat since 2019. The university also maintains academic supervision over

2112-466: The edge angle of the lens (i.e., lies outside the bandwidth of the system), is essentially wasted source bandwidth because the lens can't intercept it in order to process it. As a result, a perfect point source is not required in order to measure a perfect point spread function. All we need is a light source which has at least as much angular bandwidth as the lens being tested (and of course, is uniform over that angular sector). In other words, we only require

2176-414: The form above allows us to calculate the image plane field as the superposition of the images of each of the individual impulse functions, i.e., as a superposition over weighted point spread functions in the image plane using the same weighting function as in the object plane, i.e., O ( x o , y o ) {\displaystyle O(x_{o},y_{o})} . Mathematically,

2240-550: The function is: kr tan(Θ max ) . If Θ max is small (only a small portion of the converging spherical wave is available to form the image), then radial distance, r, has to be very large before the total argument of the function moves away from the central spot. In other words, if Θ max is small, the Airy disc is large (which is just another statement of Heisenberg's uncertainty principle for Fourier Transform pairs, namely that small extent in one domain corresponds to wide extent in

2304-682: The globe the opportunity to study at Tel Aviv University. All Lowy International School programs are conducted in English. Programs include Semester or Year Abroad, Degree Programs, and Specialized Programs, such as the International LL.M at the Faculty of Law. Students in the Undergraduate or Semester Abroad Programs are given the option of housing at the Einstein Dorms, just outside the university. Undergraduate programs: Graduate programs: Medical school: Within

2368-484: The image is expressed as: in which PSF ( x i / M − u , y i / M − v ) {\textstyle {\mbox{PSF}}(x_{i}/M-u,y_{i}/M-v)} is the image of the impulse function δ ( x o − u , y o − v ) {\displaystyle \delta (x_{o}-u,y_{o}-v)} . The 2D impulse function may be regarded as

2432-414: The image of a point object for an imaging system is a measure of the quality of the imaging system. In non-coherent imaging systems, such as fluorescent microscopes , telescopes or optical microscopes, the image formation process is linear in the image intensity and described by a linear system theory. This means that when two objects A and B are imaged simultaneously by a non-coherent imaging system,

2496-436: The image plane. It can be shown (see Fourier optics , Huygens–Fresnel principle , Fraunhofer diffraction ) that the field radiated by a planar object (or, by reciprocity, the field converging onto a planar image) is related to its corresponding source (or image) plane distribution via a Fourier transform (FT) relation. In addition, a uniform function over a circular area (in one FT domain) corresponds to J 1 ( x )/ x in

2560-410: The image plane. The argument of the function J 1 ( x )/ x is important, because this determines the scaling of the Airy disc (in other words, how big the disc is in the image plane). If Θ max is the maximum angle that the converging waves make with the lens axis, r is radial distance in the image plane, and wavenumber k  = 2π/λ where λ = wavelength, then the argument of

2624-575: The imperfect imaging of three-dimensional objects in confocal microscopy or astronomy under non-ideal imaging conditions. The ENZ-theory has also been applied to the characterization of optical instruments with respect to their aberration by measuring the through-focus intensity distribution and solving an appropriate inverse problem . In microscopy, experimental determination of PSF requires sub-resolution (point-like) radiating sources. Quantum dots and fluorescent beads are usually considered for this purpose. Theoretical models as described above, on

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2688-478: The individual astronomers such as David Polishook (see adjunct table and footnotes) . The observatory operates a 1 meter (3.3 feet)-diameter Boller and Chivens telescope , which is a wide-field Ritchey-Chrétien reflector mounted on a rigid, off-axis equatorial mount . This telescope was originally a twin of the Las Campanas 1 m Swope telescope , which was described by Bowen and Vaughan (1973), though

2752-425: The individual object-plane impulse functions are called point spread functions (PSF), reflecting the fact that a mathematical point of light in the object plane is spread out to form a finite area in the image plane. (In some branches of mathematics and physics, these might be referred to as Green's functions or impulse response functions. PSFs are considered impulse response functions for imaging systems. When

2816-400: The limit (as side dimension w tends to zero) of the "square post" function, shown in the figure below. We imagine the object plane as being decomposed into square areas such as this, with each having its own associated square post function. If the height, h , of the post is maintained at 1/w , then as the side dimension w tends to zero, the height, h , tends to infinity in such a way that

2880-448: The linearity property of optical non-coherent imaging systems, i.e., the image of an object in a microscope or telescope as a non-coherent imaging system can be computed by expressing the object-plane field as a weighted sum of 2D impulse functions, and then expressing the image plane field as a weighted sum of the images of these impulse functions. This is known as the superposition principle , valid for linear systems . The images of

2944-483: The night. Temperature gradients are small and fairly moderate. The average relative humidity is quite high, with a tendency to decline during the night from April to August. The average seeing is about 2-3 seconds of arc . A few good nights have seeing of 1" or less, while few show seeing larger than 5". An important advantage of the Wise Observatory at its location of ~35°E in the Northern Hemisphere

3008-444: The object is divided into discrete point objects of varying intensity, the image is computed as a sum of the PSF of each point. As the PSF is typically determined entirely by the imaging system (that is, microscope or telescope), the entire image can be described by knowing the optical properties of the system. This imaging process is usually formulated by a convolution equation. In microscope image processing and astronomy , knowing

3072-420: The object plane, in which case it is called shift invariant . In addition, if there is no distortion in the system, the image plane coordinates are linearly related to the object plane coordinates via the magnification M as: If the imaging system produces an inverted image, we may simply regard the image plane coordinate axes as being reversed from the object plane axes. With these two assumptions, i.e., that

3136-419: The other FT domain, where J 1 ( x ) is the first-order Bessel function of the first kind. That is, a uniformly-illuminated circular aperture that passes a converging uniform spherical wave yields an Airy disk image at the focal plane. A graph of a sample Airy disk is shown in the adjoining figure. Therefore, the converging ( partial ) spherical wave shown in the figure above produces an Airy disc in

3200-505: The other domain, and the two are related via the space-bandwidth product ). By virtue of this, high magnification systems, which typically have small values of Θ max (by the Abbe sine condition ), can have more blur in the image, owing to the broader PSF. The size of the PSF is proportional to the magnification , so that the blur is no worse in a relative sense, but it is definitely worse in an absolute sense. The figure above illustrates

3264-430: The other hand, allow the detailed calculation of the PSF for various imaging conditions. The most compact diffraction limited shape of the PSF is usually preferred. However, by using appropriate optical elements (e.g., a spatial light modulator ) the shape of the PSF can be engineered towards different applications. In observational astronomy , the experimental determination of a PSF is often very straightforward due to

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3328-404: The response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response ; the PSF is the impulse response or impulse response function (IRF) of a focused optical imaging system. The PSF in many contexts can be thought of as the shapeless blob in an image that should represent a single point object. We can consider this as

3392-463: The resulting image is equal to the sum of the independently imaged objects. In other words: the imaging of A is unaffected by the imaging of B and vice versa , owing to the non-interacting property of photons. In space-invariant systems, i.e. those in which the PSF is the same everywhere in the imaging space, the image of a complex object is then the convolution of that object and the PSF. The PSF can be derived from diffraction integrals. By virtue of

3456-544: The telescope prime focus. Since early-2009 this CCD was replaced by an SBIG STL-6303 CCD with 2048x3072 pixels, each 9 micrometers wide. The telescope and its camera, including the telescope dome, can be remotely operated. A 70 cm (28-inch) prime-focus telescope, essentially the "big brother" of the C18 and called the Jay Baum Rich Telescope (JBRT), was added in 2013. This telescope has been commissioned and

3520-422: The truncation of the incident spherical wave by the lens. In order to measure the point spread function — or impulse response function — of the lens, a perfect point source that radiates a perfect spherical wave in all directions of space is not needed. This is because the lens has only a finite (angular) bandwidth, or finite intercept angle. Therefore, any angular bandwidth contained in the source, which extends past

3584-453: The two instruments diverged somewhat during the years. It also has two CCD cameras , a two-star " Nather -type" photometer , a "Faint-object spectrograph-camera" (FOSC), and an older Boller and Chivens spectrograph . The photoelectric photometer and the Boller and Chivens spectrograph have not been in use for more than a decade. A dioptric focal reducer (Maala) was used at f/7 to project

3648-519: The university is the center of teaching and research of the city, comprising 9 faculties, 17 teaching hospitals, 18 performing arts centers, 27 schools, 106 departments, 340 research centers, and 400 laboratories. Tel Aviv University originated in 1956 when three education units merged to form the university. The original 69-hectare (170-acre) campus was expanded and now makes up 89 hectares (220 acres) in Tel Aviv's Ramat Aviv neighborhood. TAU's origins date back to 1956, when three research institutes:

3712-404: The various components in a complex optical system. A complete description of the PSF will also include diffusion of light (or photo-electrons) in the detector, as well as tracking errors in the spacecraft or telescope. For ground-based optical telescopes, atmospheric turbulence (known as astronomical seeing ) dominates the contribution to the PSF. In high-resolution ground-based imaging, the PSF

3776-418: The volume (integral) remains constant at 1. This gives the 2D impulse the shifting property (which is implied in the equation above), which says that when the 2D impulse function, δ( x  −  u , y  −  v ), is integrated against any other continuous function, f ( u , v ) , it "sifts out" the value of f at the location of the impulse, i.e., at the point ( x , y ) . The concept of

3840-440: The world and third in Israel in its 2016 CWUR World University Rankings. They have also ranked it as 56 in 2012. The Times Higher Education World University Rankings for 2019 placed Tel Aviv University at 189th in the world. The ratings reflect an overall measure of esteem that combines data on the institutions' reputation for research and teaching. In 2016 QS World University Rankings ranked Tel Aviv University 22nd in

3904-662: The world for citations per faculty, which is the indicator that measures a university's research impact. This makes Tel Aviv University the leading university in Israel in terms of research. In 2015 the Academic Ranking of World Universities gave Tel Aviv University the following subject rankings: 20th in Computer Science, 51–75 in Mathematics, 76–100 in Physics and 76–100 Economics/Business. In 2016 it

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3968-455: The years, most of the observing time during a given period has been allocated to one or two large, long-term, projects carried out by Tel Aviv faculty and graduate students. Tel Aviv University Tel Aviv University ( TAU ) is a public research university in Tel Aviv , Israel. With over 30,000 students, it is the largest university in the country. Located in northwest Tel Aviv,

4032-613: Was added to the Wise Observatory in 2005 mainly for minor planet CCD photometry purposes and funded by the Israel Space Agency as part of a National Knowledge Center on Near Earth Objects. This is a Centurion-18 (C18) that has been extensively modified by the observatory staff in a continuous effort to transform it into a robotic telescope . The telescope was originally equipped with a thermoelectrically cooled SBIG ST-10XME CCD camera with 2184x1472 pixels each 6.8 micrometres wide, each subtending slightly more than one arcsec at

4096-496: Was ranked as 51–75 in Engineering. From the year 2007 until 2018, Tel Aviv university ranks as 35th in the world in Computer Science according to CSRankings, the same rank as Harvard and the second-highest ranked in Israel. As of 2021, it is ranked as the 191st best university in the world by THE World University Rankings , 230th by the QS World University Rankings and in the 151–200th bracket by

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