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Echelle gratings are useful in planet-finding astronomy, and are used on the successful HARPS and PARAS (PRL Advanced Radial-velocity All-sky Search) spectrograph.

Diffraction angles at the grating are not influenced by the step structure. They are determined by the line spacing and can be calculated according to the in-plane version of the grating equation:

Knowledge of electromagnetic waves and mathematical tools at the level of a senior electrical engineering undergraduate are assumed.

The courses in this specialization can also be taken for academic credit as ECEA 5600-5602, part of CU Boulder’s Master of Science in Electrical Engineering degree. Enroll hereOpens in a new tab.

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This Specialization is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹

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Analyze you designs in an industry standard optical design code, OpticStudio by Zemax, to validate and optimize the design

A blazed grating – also called echelette grating (from French échelle = ladder) – is a special type of diffraction grating. It is optimized to achieve maximum grating efficiency in a given diffraction order. For this purpose, maximum optical power is concentrated in the desired diffraction order while the residual power in the other orders (particularly the zeroth) is minimized. Since this condition can only exactly be achieved for one wavelength, it is specified for which blaze wavelength the grating is optimized (or blazed). The direction in which maximum efficiency is achieved is called the blaze angle and is the third crucial characteristic of a blazed grating directly depending on blaze wavelength and diffraction order.

Like every optical grating, a blazed grating has a constant line spacing d {\displaystyle d} , determining the magnitude of the wavelength splitting caused by the grating. The grating lines possess a triangular, sawtooth-shaped cross section, forming a step structure. The steps are tilted at the so-called blaze angle θ B {\displaystyle \theta _{B}} with respect to the grating surface. Accordingly, the angle between step normal and grating normal is θ B {\displaystyle \theta _{B}} .

This Specialization is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹

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Optical instruments are how we see the world, from corrective eyewear to medical endoscopes to cell phone cameras to orbiting telescopes. This course will teach you how to design such optical systems with simple graphical techniques, then transform those pencil and paper designs to include real optical components including lenses, diffraction gratings and prisms. You will learn how to enter these designs into an industry-standard design tool, OpticStudio by Zemax, to analyze and improve performance with powerful automatic optimization methods.

The blaze angle is optimized to maximize efficiency for the wavelength of the used light. Descriptively, this means θ B {\displaystyle \theta _{B}} is chosen such that the beam diffracted at the grating and the beam reflected at the steps are both deflected into the same direction. Commonly blazed gratings are manufactured in the so-called Littrow configuration.

A special form of a blazed grating is the echelle grating. It is characterized by particularly large blaze angle (>45°). Therefore, the light hits the short legs of the triangular grating lines instead of the long legs. Echelle gratings are mostly manufactured with larger line spacing but are optimized for higher diffraction orders.

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In each course of this Specialization, you will design progressively more complicated optical systems, like those you will find in the real world. To do so, you will use both basic mathematical tools and the software application OpticStudio, made by Zemax for the final design.

Yes! To get started, click the course card that interests you and enroll. You can enroll and complete the course to earn a shareable certificate, or you can audit it to view the course materials for free. When you subscribe to a course that is part of a Specialization, you’re automatically subscribed to the full Specialization. Visit your learner dashboard to track your progress.

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This program is part of the University of Colorado Boulder's Master of Science in Electrical Engineering, a fully MOOC-based master's degree offered in partnership with Coursera. In addition to the coursework in this non-credit specialization, which will transfer to your for-credit course, if you pay tuition and pass all required for-credit work in each course, you will earn CU Boulder academic credit and can potentially apply that credit toward a degree. Learn more, and start your journey today.

The Littrow configuration is a special geometry in which the blaze angle is chosen such that diffraction angle and incidence angle are identical.[1] For a reflection grating, this means that the diffracted beam is back-reflected into the direction of the incident beam (blue beam in picture). The beams are perpendicular to the step and therefore parallel to the step normal. Hence it holds in Littrow configuration α = β = θ B {\displaystyle \alpha =\beta =\theta _{B}} . All other geometries yield anamorphic Littrow expansion or compression of the beam.

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Develop strategies for correcting aberrations and enhancing the performance of optical instruments in various applications

This course is completely online, so there’s no need to show up to a classroom in person. You can access your lectures, readings and assignments anytime and anywhere via the web or your mobile device.

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. If you only want to read and view the course content, you can audit the course for free. If you cannot afford the fee, you can apply for financial aidOpens in a new tab.

Blazed gratings can also be realized as transmission gratings. In this case the blaze angle is chosen such that the angle of the desired diffraction order coincides with the angle of the beam refracted at the grating material.[2]

For the Littrow configuration, this becomes 2 d sin ⁡ θ B = m λ {\displaystyle 2d\sin {\theta _{B}}=m\lambda } . By solving for θ B {\displaystyle \theta _{B}} the blaze angle can be calculated for arbitrary combinations of diffraction order, wavelength and line spacing: