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Stephen Remillard
United States
Приєднався 26 лис 2020
Physics and engineering videos made either for specific courses or simply to satisfy an interest.
Good luck with your project! Regrettably, I won't have the time to help with it.
Good luck with your project! Regrettably, I won't have the time to help with it.
Three Types of Image Smear
Linear motion is a major issue with pixel smear, especially in the case of satellite remote sensing, which is used here to illustrate smear. I may get around to doing another video for jitter and oscillation, depending on how well this one is received.
The degrading effect of smear is measured through its impact on contrast, which is gauged by the modulation transfer function (MTF). So, I talk about that here.
We are in the middle of a module on optical detectors and focal plane arrays. So, because you are "sitting in" on a mid-course lecture, there could be some unfamiliar terms and concepts. This lecture assumes some familiarity with MTF, the influence of pixel size on MTF, and the cut-off spatial frequencies that define the loss of contrast. That's where it picks up.
This shameless promotion is snipped from my 10-week course on optical systems engineering that is open to anyone who has taken a university-level course on optics. This on-line course has weekly Zoom sessions and a lively course discussion board, gets you to do homework which receives ample feedback from me, is a great networking opportunity, and comes with about 12 hours of recorded lectures, of which this video is a sample. Google my name along with "optical systems engineering course" to learn more.
ce.uci.edu/courses/course-details?eventId=EECS_X496
The degrading effect of smear is measured through its impact on contrast, which is gauged by the modulation transfer function (MTF). So, I talk about that here.
We are in the middle of a module on optical detectors and focal plane arrays. So, because you are "sitting in" on a mid-course lecture, there could be some unfamiliar terms and concepts. This lecture assumes some familiarity with MTF, the influence of pixel size on MTF, and the cut-off spatial frequencies that define the loss of contrast. That's where it picks up.
This shameless promotion is snipped from my 10-week course on optical systems engineering that is open to anyone who has taken a university-level course on optics. This on-line course has weekly Zoom sessions and a lively course discussion board, gets you to do homework which receives ample feedback from me, is a great networking opportunity, and comes with about 12 hours of recorded lectures, of which this video is a sample. Google my name along with "optical systems engineering course" to learn more.
ce.uci.edu/courses/course-details?eventId=EECS_X496
Переглядів: 148
Відео
What is the Refractive Index of Air?
Переглядів 27921 день тому
Well, to four significant figures it's n=1. But, in this video I look at why that little bit of air refraction matters in optics, and why it happens. Sources: Publications Hopfield, Helen S. "Tropospheric refraction effects on satellite range measurements." APL Technical Digest 11 (1972). secwww.jhuapl.edu/techdigest/Content/techdigest/pdf/APL-V11-N04/APL-11-04-Hopfield.pdf Pollinger, F. (2018)...
Four Types of Image Vignetting
Переглядів 4342 місяці тому
Four different ways that a camera can vignette an image are described. This video is snipped from a lecture in my Optical Systems Engineering course ce.uci.edu/programs/engineering/optical-engineering Please consider clicking on "Like" so that I know what sort of content is being appreciated. #lensdesign
Three Types of Image Distortion
Переглядів 6543 місяці тому
Computation and interpretation of distortion aberration are explained and demonstrated with a ynu spreadsheet in Excel. Zemax OpticStudio from Ansys is used to check the results. You can learn more about the effect of aberrations, among other things, on image quality in my course on optical systems engineering: ce.uci.edu/courses/course-details?eventId=EECS_X496 OpticStudio is a product of Ansy...
Paraxial Ray Tracing Using Matrices, with a FRED Example of a Cassegrain Telescope
Переглядів 1,1 тис.9 місяців тому
The ray tracing matrices are explained, emphasizing the reflection matrix. I find the system matrix for a Cassegrain telescope with an eyepiece and use it to compute the correct location of the eyepiece. The result is confirmed by simulating it in FRED. Although suitable to watch alone, this is a continuation of the video: ua-cam.com/video/LnnYwbhP7w4/v-deo.html FRED is a product of Photon Engi...
The optical path length of a vacuum-spaced Fabry-Perot interferometer
Переглядів 1,3 тис.Рік тому
Answer to a viewer's question about finding the optical path length difference between two interfering rays in a Fabry-Perot interferometer. I changed the title of this video by replacing "air-spaced" with "vacuum-spaced" since the analysis was done using a refractive index of exactly 1. Please consider clicking on "LIKE". I don't get paid for creating this content, and your positive feedback i...
Write your own program for optical ray tracing - Here's mine in MatLab
Переглядів 5 тис.Рік тому
Viewers have asked me to describe my homemade MatLab function that performs ray tracing on a refractive lens system. The program can sequentially analyze an arbitrary number of lens elements with an aperture stop located anywhere along the lens. Aberration coefficients are computed, along with Petzval radius and distortion percent. System properties (aperture metrics and field metrics) are also...
Microlithography Reduction Projection Stepper Lens Design: A Patent Study
Переглядів 2,3 тис.Рік тому
I worked through a stepper lens patent application, and here is what I learned. A little bit about the lens. A little bit about microlithography. "Microlithography Reduction Projection Stepper." That's a lot of words modifying the one little word "lens". I just threw them all in there:) Optical Design Playlist: ua-cam.com/play/PLmfHzApbF5dbx_S_h9A13uLm4LVK0f6XK.html Please consider clicking on ...
Telephoto Prime Lens Design: A Patent Study
Переглядів 6 тис.Рік тому
This fourth patent study in devoted exclusively to one patent, both because of the detailed review I wanted to do, and because it is such a good patent with good embodiments. Some topics covered in this video that I haven't touched on before include stray light analysis, wave front error, and depth of field. Please consider clicking on "LIKE". I don't get paid for creating this content, and you...
Anamorphic Prism Design: A Patent Study
Переглядів 1,8 тис.Рік тому
Mixed mode ray tracing using Zemax OpticStudio. That could be the subtitle. Design examples are presented from two different patents for anamorphic prisms that turn cylindrical profile beams into circular profile beams. The first patent is a single anamorphic prism and the second design is an anamorphic prism pair. The simulation is done in mixed mode (or hybrid mode) - that is sequential ray t...
Smartphone Camera Lens Design: A Patent Study
Переглядів 13 тис.Рік тому
I dissected a recently issued patent for a 6-element smartphone camera lens. As much was learned about mobile phone cameras in general as about the patent itself. I always find some kind of typo. There is one at 3:28. The "r" in the sag equation is actually a "y". OpticStudio is a product of Zemax (www.zemax.com) Please consider clicking on "LIKE". Your positive feedback is the only encourageme...
Electronic Viewfinder Eyepiece Design: A Patent Study
Переглядів 1,9 тис.Рік тому
I loaded the specs from an electronic viewfinder patent into Zemax OpticStudio, and this is what I found. A quick comparison will be made with near-eye displays. Some features of OpticStudio will also be explored, including coordinate breaks, the multiconfiguration editor, and optimization. The eyepiece patent is US Patent number 8,531,774 B2. The head mounted display patent is US Patent number...
The Third Order Aberration Coefficients of Aspheric Surfaces
Переглядів 1,6 тис.Рік тому
In this video, you will find the expressions for the aspheric corrections to the third order Seidel coefficients for the five geometric aberrations. Example calculations for an aspheric reflector and for an aspheric lens are presented. Sorry about the somewhat poor screen resolution. Somehow I managed to upload this video at only 480p. Not the best resolution for spreadsheets. Please consider c...
The Fabry-Perot Interferometer: What Do the Fringes Mean?
Переглядів 6 тис.Рік тому
So, you are doing your pre-lab due diligence for a Fabry-Perot experiment. You're not alone if you don't see a straight line between the descriptive mathematics and the fringes. I did some soft experiments to help me to recognize the meaning of the fringes. There are a lot of variables to control in a real experiment and running simulations can be so helpful because you can know and control the...
Transmission and Reflection at a Potential Barrier
Переглядів 4,3 тис.Рік тому
The transmission and reflection coefficients for a probability wave at a step in potential are derived and explained. This is an excerpt from one of my Modern Physics lectures. Please consider clicking on "Like" so that I know what sort of content is being appreciated. I don't ask for support for developing this content, just the satisfaction of knowing that it is appreciated. #GriffithsQuantum...
Telecentricity: A Tutorial using Excel
Переглядів 1,4 тис.2 роки тому
Telecentricity: A Tutorial using Excel
How Do You Measure the Width of a Laser Beam?, PHYS 382
Переглядів 3,2 тис.2 роки тому
How Do You Measure the Width of a Laser Beam?, PHYS 382
The Quality Factor (Q) of a Quarter-Wave Coaxial Microwave Resonator
Переглядів 2,4 тис.2 роки тому
The Quality Factor (Q) of a Quarter-Wave Coaxial Microwave Resonator
Measuring the Refractive Index of Glass using a Michelson Interferometer, PHYS 382
Переглядів 3,2 тис.2 роки тому
Measuring the Refractive Index of Glass using a Michelson Interferometer, PHYS 382
Computing Petzval Curvature - 3rd Order Field Curvature Aberration
Переглядів 2,2 тис.2 роки тому
Computing Petzval Curvature - 3rd Order Field Curvature Aberration
Why Does a Michelson Interferometer have a Bull's-Eye Interference Pattern (sometimes)?
Переглядів 4,5 тис.2 роки тому
Why Does a Michelson Interferometer have a Bull's-Eye Interference Pattern (sometimes)?
Aligning an Infrared Michelson Interferometer, PHYS 382
Переглядів 4,1 тис.2 роки тому
Aligning an Infrared Michelson Interferometer, PHYS 382
The Finite Square Potential Well Transmission Coefficient
Переглядів 4 тис.2 роки тому
The Finite Square Potential Well Transmission Coefficient
Measuring Noise Figure using a Spectrum Analyzer - The Gain Method
Переглядів 11 тис.2 роки тому
Measuring Noise Figure using a Spectrum Analyzer - The Gain Method
How Does an Aperture Stop Influence Third Order Lens Aberrations? A Tutorial using Excel
Переглядів 1,5 тис.2 роки тому
How Does an Aperture Stop Influence Third Order Lens Aberrations? A Tutorial using Excel
Chromatic Aberration: Calculating the Lateral Color of a Lens
Переглядів 1,7 тис.2 роки тому
Chromatic Aberration: Calculating the Lateral Color of a Lens
Computing the Third Order Spherical Aberration of a Lens
Переглядів 3,5 тис.2 роки тому
Computing the Third Order Spherical Aberration of a Lens
The Cooke Triplet: A Paraxial Ray Trace Example
Переглядів 2,8 тис.2 роки тому
The Cooke Triplet: A Paraxial Ray Trace Example
Optics is a complicated Physics
I couldn't find the expression for CTR in the later part of the video, did i miss any part....?
The Excel formula in Cell I22 for CTR is =-F12*F15*(E10+F10-(E18*F10*E10))/I7 The mathematical expression for CTR is found at 3:38.
Dear Stephen, Thank you for great explanation. I couldn't find related excel. Is there any way to download it? Regards
Fantastic explanation. Many thanks!
I am a bit confused about Idsat. What if instead of evaluating it at x=L , we evaluate it at x=0. Idsat should be the same regardless of x. Then Idsat= wCox(Vgt-Vcs(0))vsat, which is completely different?
Very important video for laser diode application. Thank you.
Fantastic explanation! Cheers!
Could we offset some of these exagerated aberrations by utilizing curved first surface mirrors to zero out said distortions? I assume this wont work with mustache distortion . Could one further reduce these distortions by subsequently switching to a monochrome approach using monochrome light and complimentary optical filters on the lens?
I was making the exact same mistake as the viewer haha. I even asked chat gpt and it told me that it should indeed be 2d/cos(theta). However I was sceptical and luckily found your explanation. Thank you sir!
Hello Stephen. It seems to me that such a large number of glass-air-glass transitions will change all theoretical calculations to Zero due to re-reflections of glass surfaces. I'm a photographer, but I'm interested in microphotography. Eduard.
It is a lot of surfaces isn't it. With 58 surfaces each having a 1% AR coating the back-of-the-envelope transmission is at best 0.99^58=56%. Not zero, but still a lot of loss. I'm not really sure if anything else is typically done to reduce loss with so many elements. The stray light from these reflections is probably no trivial matter either.
@@stephenremillard1 Yes, scattered internal light will also lead to a significant decrease in contrast, halos and blur at the borders. And this is the most necessary thing in lithography, a clear/sharp separation from dark to light. It would be interesting to see an image from this lens on a matrix camera. Creating one copy of a lens is an expensive pleasure. Only an enthusiast who risks time and expense will be able to do this.
@@stephenremillard1 Maybe look at this with lens blocks immersion glued on. You may end up with universally changeable options.
Thank you so much for the video. I was wondering if there are any books you can recommend on this subject? Thanks in advance. I really appreciate your work.
Yes, and I think it would be really great if other viewers could chime in here with their own recommendations. I got a lot out of the treatment in Saleh and Teich, and also from Pedrotti, Pedrotti, and Pedrotti. But there was also plenty that I learned from experimentation, and I admit I have lost track of specifically what I have learned from reading and what I learned from experimentation. And when I say experimentation I am referring to both hard and soft experiments (hardware and software), but mostly soft experiment for me on this topic. And actually it's the soft experiments where you learn a lot and learn it quickly because it's versatile and quick, and you can immediately understand your results. For me there was the use of MatLab and also the use of nonsequential ray tracing, both of which I demoed a little bit in the video. But of course you're right in hitting the books first to get the foundational knowledge that you can then knowledgeably use in those experiments.
Thanks you!!!
Thankyou for making this. Very fun to watch. The fine structure constant isn't as constant as advertised. I'm glad you commented that it doesn't matter what [a] constant is, it matters that it is "constant."
It's a little bit different from what I taught myself using quadratics. That one in the middle (9:46) is a Second Kind type, or Fibonacci-like discrete homogenous sequence, even though it has that plus sign. That would make the magnitude equal to one, but that can be manipulated to r^((t-1)/2). I don't know how that changes, given the outside term. Is that a cubic? Are they triangle waves in 3d? The 'e' on the outside is vector angle addition. The magnitude is 1. That one is easier, r^t. There should be another function that pairs with this. Ψ(n+1)+Ψ(n-1)+f(n)=0 (I'm too lazy to do notation correctly). I might be wrong though, given that it is cubic. Anyway, that's wrong. You can't do the 2cos(dwt-dkx) thing. ChatGPT always simplifies that function, but it's wrong, I checked. It will work if time and displacement is an integer. It becomes a complex number when they are rational (fractional). 2cos(dwt-dkx) doesn't appear to become a complex number. Standup Maths: "Complex Fibonacci Numbers" kind of addresses it. Ψ(n+1)/Ψ(n) where n = -2 -i*2.. 2+i*2 should be a magnetic field. Three poles, I'm guessing, project it on a sphere. You might need to customize the tool you use to graph it because it's cubic.
Thankyou for the video. I can't see Lambda and not think, λ = (h/p), I like their version: λ /NA, just use 193nm/1.55. That made me giggle.
I can't find the double like button. Thanks for video!!
Thank you very much for the Video. For the same case: Would it be reasonable to use the method from the paper "Characterization of High- Resonators for Microwave-Filter Applications" by Raymond S. Kwok and Ji-Fuh Liang (1997)?
Yes sir. I think so.
So this formula (Insertion loss method) breaks down for the case of a critically coupled resonator, because the when Li approaches 0, Qu should be double of Ql and not go to infinity. Is there a relation taking into account strong coupling near critical coupling or am I missing something obvious?
I have always avoided critical coupling for my purposes, so maybe let's see what someone else says. But the insertion loss, Li would only ever be exactly zero at critical coupling if there were actually no dissipation, hence infinite unloaded Q. So, I don't find it alarming that Q blows up for zero Li at critical coupling. What is not baked into the equation is what the loaded Q should be at critical coupling if there were no dissipation, since in that specific case loaded Q is the product of zero and infinity. I am not familiar with the argument that the loaded Q is half the unloaded Q at critical coupling. In my experience, those two numbers diverge as critical coupling is approached from below.
@@stephenremillard1 But wouldn't he dissipation be dependent on the linewidth of the resonance and not the amplitude? I question myself what would happen at high coupling that approaches critical coupling. From theory I know that the linewidth of the resonance would increase. I found in literature that at critical couplings the linewidth is twice the unloaded linewidth. This comes from the definition of critical coupling: "A condition in a resonator system where the rate of energy transfer to an external load matches the intrinsic loss rate within the resonator, leading to maximum energy transfer and minimal reflection at resonance.". And in the very weak coupling regime one would measure the approximately the unloaded linewidth. But I believe there should be an expression for the calculation of the unloaded linewidth of a system with strong coupling, by knowing the amplitude at resonance. Do you know something that could help me?
@Stephen Remillard. Hi Stephen, I am a student in optics.Could you explain the equation at line and 142 of your code (@15:11); In this section I don't konw the value EFL why not mentioned here?Also,I couldn't find the new variable EFL you used in line 159 (@15:49) in the previous code ? Please tell me the reason.
The quantity that is computed in the loop from lines 136 to 138 isn't the complete total track length. It is only the distance up to the last glass vertex. The back image distance still needs to be added to it in order to have the quantity that is typically referred to as total track length. The effective focal length is calculated on Line 152 (@15:37).
@@stephenremillard1 Thank You for your expaining, The problem has been solved。 But have a new problem , when I using your all code for learning MATLAB and Optical fundamental konwledge , the speed for program is to slowly .I let this code run for 15 minutes, and the code still has not jumped out of 44 lines of code to find the loop of the chief ray.(@8:23)
@manarc-cs6uv It sounds like the loop termination condition is either being missed, or not reached. You might try changing the size of the variable incr. Increase it a factor of 10 or decrease it a factor of 10. Then try factors of 100 or more if that doesn't work. If it is taking too long to complete the loop, then incr is too small. If it never completes, then incr might be too large - which is why I had to give it a small value.
I'll also add that a better programmer than I can come up with a better way to execute that operation in the red box @8:23. A while loop isn't very efficient, and is perhaps evidence of my Fortran 77 upbringing.
@@stephenremillard1 I tried the variables of reduction and enlarging INCR again, but it still seemed to be unable to meet the condition in the WHILE loop Done == 1.
Thank you for this video!
Beautiful work. Thankyou! You are an absolute treasure. As a computer scientist all I see are chains of matrix operations :)
Thanks for the nice compliment. If you can see the matrix operations, then you're the real deal, because that's exactly right.
Thankyou Your videos are incredible
Thank you so much. You are a fantastic teacher
Stephen this is great information. Thank you for explaining this. Oddly, I am looking to introduce sagittal astigmatism preferably with AR/AS coatings. Do you know what type of optic I should be looking at (specific name / keywords) and where to source this? I've used these terms with no results. I am looking for an 82MM diameter optical filter that can effectively swirl the edges of my frame with preexisting lenses. Thanks for your help!
This sounds like a job for either a cylindrical lens or an aspheric lens, both of which can be purchase from Thorlabs (www.thorlabs.com/navigation.cfm?guide_id=2087). You can specify an AR coating when ordering. Not sure about AS coatings though. I would probably go with a cylindrical lens element with a fairly large radius of curvature (www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=2803). This way you introduce a small anamorphic effect. That's my spur-of-the-moment thought on the matter.
Thanks! I came out confused from my quantum class and this was very helpful!
Wow! The electron tunneling equation looks cool!
Hi stephen! Is there a way in contacting you? Im doing the same experiment in uni but im having problems getting the info of the laser/bullseye on the arduino camera. How did you get the data?
What is your opinion of Leica Co working with Xiaomi?
Stephen you always much such great and clear videos! please keep up the great work.
I wonder why plastic is not used for photograph lenses in larger formats.
Small range of refractive index, high coefficient of thermal expansion and poor optical properties I have seen plastic lenses on aliexpress, they have poor quality but low price
It is - canon has got quite good at moulding elements at that size, so their cheap lenses tend to include some very extreme plastic aspherics (e.g. the RF 28mm f/2.8)
Please continue Your helping me and Many others unravel The process of lens Design in the digital image capture.
Great presentation! Thank you for showing the simulation results. Much easier to understand the discussion by seeing pictures
Very good descriptions
I will be using pyramidal horn antennas with an LNA and a spectrum analyzer to scan in a 360 degree azimuth to look for possible interference in the X and S bands (2GHz and 8GHz). One of the requirements is to "Calculate cold sky noise temperature at 10 degree elevation." Would you (or anyone) perhaps know how one does this? Is this simply measurable somehow? Google doesn't get me too far...😕
I'm in the same boat as Google. Not really something I know how to do.
@@stephenremillard1 ok, thank you.
@@j.w.8663 I wish I could be more helpful. Your question did stir up a memory for for me, though. When I was in grad school I had some microwave measurement questions, and I contacted someone at NRAO (National Radio Astronomy Observatory) who was very helpful. I even went to visit since I was close. It impressed me how eager these guys were to be a resource for a student. I'm going to guess that there is well-established know-how for your specific question that resides squarely in the radio astronomy community. I don't work in that field, but it does have a wealth of knowledge about microwaves, the sky, noise, etc.
The video you made is really good! I just started to learn to use ZEMAX software. In front of you, I feel like I am like a boat that has just been launched, and there is a long way to go. Thanks you !
Excellent video on such important topic for laser diodes. Is it possible to use the Achromatic Anamorphic Prisms pairs of the same glass type and get great beam spot size? Why two different glass types are needed?
Using two glass types helps to keep the outgoing angle and height the same for all wavelengths. But as I found, it isn't perfect. You certainly can use two prisms of the same glass type, which just means a little more variation with wavelength in the outgoing angle. Using two different glasses doesn't affect the beam quality for monochromatic light, but it does help to keep all colors on the same path if the spectrum is broad.
Thanks for these videos. I wish I had seen these 30 years ago!
How I can get this excel file?
20 minutes and it solves my 2-day problem. Big thanks!
Excellent!
Great video. Thank you for sharing.I have to watch it again to understand more than 10%😂
16:09: Dr. Remillard says "the group velocity is LESS than the phase velocity", which I believe was a mistake, since it's written that the group velocity is GREATER than the phase velocity, which is true for d v_p / d omega > 0.
You are right. What is written is correct. Thanks for pointing that out.
Thanks for wonderful video but I am still a little confused that the magtify of distortion should change following the curve of lens shape but how can you get a number telling about distortion since lens 5 and 6 are not spherical lens so distortion might change from barrel to pincushion based on how chief ray is reflacted on curve, can you help me to get deeply in it? I am college student and trying to research about distortion, thank you alot
This is a really good question. Wavefront aberration coefficients can be computed analytically through fourth order aspheric. But for higher order aspherics, ray tracing is exclusively used to understand the final image locations. A fourth order aspheric will cause a small departure from a spherical surface, unlike the higher order terms in the surfaces used here. As you noted, the distortion is hybrid, meaning that there is a change in sign moving from the center to the image edge, and ray tracing, rather than a single number such as a Seidel coefficient, is the only way to look at it. Zemax, and all other programs, do compute a table of Seidel coefficients. But when higher order aberrations dominate, and high order aspherics are used, I really don't know what meaning, if any, they have. I'm sure they are meaningful, and maybe someone can help us out here. By the way, you can get hybrid distortion without using aspherics. Some lenses balance out the third order distortion leaving higher order field dependent magnifications that can result in a wavey distortion versus field plot. Bear in mind that a distortion plot is not the result of only the third order polynomial term, but of all polynomial terms that describe a displacement in the chief ray.
@stephenremillard1 thank for great explaination, I did some experiments in cooke triplet lens structure and realize that distortion's magnitude is really hybrid through lenses but in another lens structure, it not really working that way, when the system get signigiciant magnitude on barrel distortion, I add into it another got barrel distortion lens and the final result make the distortion decreased but image smaller, this is quite interesting, the image is really compressed to expand FOV with lower distortion. But I still dont know the way it works.
Do you have resource recommendations to get started?
As much as I would really like to say that you can master this craft by watching my UA-cam videos, that probably won't do it. So, you are right in looking for resources. I think it's critical to engage, use software, follow guidance from knowledgeable teachers, and collaborate with a cohort. After all, expertise only comes with a lot of practice. There are courses at UDEMY, CourseEra, UC Irvine DCE, and others, and which is best depends on your background (science, art, etc) and where you want to go with this knowledge (lens design, photography, etc.).
@@stephenremillard1 Thanks for the response I will check them out. While I do have a stem (biochem) background did cover maths and physics, we didn't touch on optics a whole lot. I am a hobby photographer and microscopist, lens design is something that interests me and understanding it surely will come in handy as well. I subscribed to you, I'm sure I can at least pick up some things listening to someone so knowledgeable!
Hello I need and answer to this important question if a mosfet is rating at 94amp and 380 amp pulse current at 580watt power dissipation rating if the frequency is 250khz does the current rating remain the same or it reduces the current rating please explain to me thank you
@Stephen Remillard. Could you explain the equation at line and 49 of your code (@7:18)? How did you come to this equation? thanks in advance!
Take a look at 3:46. This is the equation at the top of the screen, (n'u'=nu-y*phi). In Line 49, yt(i) is the chief ray height at surface i. uprime is the chief ray angle after the designated surface. So, uprime(i-1) is the chief ray angle incident at surface i, since it is the chief ray angle after surface i-1. Also, the angles are replaced with tangent of the angles to improve the accuracy.
Thank you!!
wonderful