The Deep-sky Imaging Primer – Third Edition

Over ten thousand people got their start in astrophotography with the first two editions, now The Deep-sky Imaging Primer has been fully revised and expanded in this new third edition. It has been updated to include the latest cameras, technology, and software. Everything you need to know about capturing and processing stunning images of deep-sky objects is covered:

  • The fundamental principles of electronic cameras, optics, and mounts
  • How to choose the best camera and telescope for you
  • How to set up, choose exposure parameters, and take the images
  • Where and when to find the best deep-sky objects
  • How to process images—in addition to PixInsight® and Adobe Photoshop®, Affinity Photo® and AstroPixelProcessor® are now fully covered

Start-to-finish examples of image processing are included, with a focus on PixInsight. The book is 280 pages with 373 illustrations, printed in full-color.

There are two ways to purchase a copy:

  1. You can buy a printed copy at Amazon (affiliate link; I earn a few extra cents).  List price is $49.99.
  2. By popular request, it is also now available as a personalized pdf for $29.99.  This includes a bonus chapter, and it’s best viewed on a laptop or full size tablet (not a mini or phone), as it retains the two-column layout of the printed book.  If you’re interested, send PayPal payment to me at deepskyprimer@gmail.com with your name and the email address you want me to send the book to. (If you don’t have Paypal, send me a note, and I can send you a link to pay via credit card.) I can usually turn them around in a day, but it may take up to a week if I’m traveling when your order comes in.  

I’m happy to answer any questions at deepskyprimer@gmail.com.

 

The complete Table of Contents is listed below.

Welcome to Astrophotography!    7

Section 1: Understanding Images

  1. Electronic sensors
    • The challenges of deep-sky imaging 9
    • How electronic sensors work                   9
    • Sensor architecture: CCD vs CMOS      10
    • Well capacity and bit depth   11
    • The trade-off between dynamic range and gain              11
    • The importance of bit depth 13
    • Linear data and response curves          13
    • Creating color images                14
  2. Signal and Noise
    • How signal varies       16
    • Signal and noise at the pixel level        17
    • Shot noise    18
    • An example of shot noise        19
    • A dimmer example   22
    • Skyglow        22
    • Why shot noise cannot be subtracted away    23
    • Dark current                   24
    • Read noise   25
    • Adding signals and noise        26
    • Variation in two-dimensions                    27
    • Bringing it all together              27

Section 2: Acquiring Images

  1. Choosing and using a mount
    • Types of mounts                  31
    • Choosing and using a GEM              33
    • Meridian flip        33
    • Polar alignment 34
    • Drift alignment 35
    • Impact of polar alignment error on tracking            35
    • Tracking error     36
    • Balancing a mount             37
  2. Choosing a camera
    • DSLRs    38
    • Dedicated astronomical cameras                  38
    • Parameters to consider in choosing a camera         39
    • The CMOS revolution       39
    • Sensor size and field of view          39
    • Parameters of common sensors  40
    • Connecting your camera to a telescope   42
  3. Image scale: matching sensor and optics
    • Resolution and seeing     43
    • Sampling               45
    • Factors that limit resolution          46
    • Equipment recommendations     48
    • Focal reducers and field flatteners               48
    • Finding the right flattener or reducer        49
    • Understanding the ‘f-ratio myth’ debate 50
    • Etendue and comparing optical systems 50
  4. Choosing a telescope
    • Fundamental optical parameters                  52
    • Telescopes for visual vs. imaging use         52
    • Optical aberrations            52
    • The Strehl ratio 54
    • Refractors              54
    • Telephoto lenses                 56
    • Reflectors and compound telescopes        56
    • Summary of telescope options    59
  5. Filters and narrowband imaging
    • Filters for imaging             60
    • Choosing the right filter size          60
    • Narrowband filters             61
    • Light pollution filters       63
    • DSLR filters and modification       64
  6. Focusing and setting up
    • Focusing                 65
    • Achieving critical focus  65
    • Reducing setup time        66
    • Dovetails, rings, and other mount accessories       67
    • Threaded connections    67
    • Power supplies  68
    • Dew prevention                    68
    • USB cables and hubs         68
  7. Automating image acquisition
    • Automating your imaging               69
    • Connecting to the mount                 70
    • ASCOM, Alpaca, and INDI                 70
    • Choosing and setting up a control PC         71
  8. Autoguiding
    • Autoguiding fundamentals            73
    • Autoguiding software     74
    • Guiding graphs and performance                 76
  9. Setting exposure parameters
    • Principles of choosing subexposure duration         78
    • Subexposure duration: the histogram method      79
    • Subexposure duration: the calculated method     79
    • Setting gain         82
  10. Taking the exposures
    • Planning for a night of imaging  84
    • A basic image capture workflow 85
    • A review of calibration frames     85
    • Taking dark frames            87
    • Taking flat frames               87
    • How many flats should you take?                  88
    • Taking bias frames             88
    • Do I really need to take calibration frames?              89
    • Dithering light frames     89
  11. Choosing objects to image
    • The size of deep-sky objects          90
    • The deep-sky catalogs    90
    • Object types and the seasons        91
    • A survey of object sizes  94
    • Giant Objects (2° or greater)           94
    • Really Big Objects (1–2°)                    94
    • Objects from 30–60’          94
    • Objects from 15–30’          95
    • Objects from 5–15’             95
    • Objects from 1–5’                95
    • Objects smaller than 1’   95
  12. The Sun, the Moon, and the atmosphere
    • When is it dark enough? 96
    • Light pollution  96
    • Measuring sky brightness                98
    • Impact of the moon           98
    • Impact of object altitude                  99
    • Local turbulence                  101
  13. Improving your results
    • The astrophotography learning curve       102
    • Getting more data              102
    • Getting better SNR from your raw data     102
    • Getting better resolution                 103
    • Getting more out of your data in processing            103

Section 3: Processing Images

  1. Color in digital images
    • Raw data and image file formats                    105
    • How we perceive color    105
    • Producing color on print and screen           105
    • Color management and color spaces          107
    • LAB color                108
    • The HSL/HSV/HSB color model    108
    • White balance and color temperature       108
    • Deep-sky color accuracy 109
    • Color calibration with stellar spectra          109
  2.  Image processing applications
    • The stages of image processing  110
    • Choosing among image processing applications 110
  3. Using Pixinsight
    • PixInsight’s learning curve              112
    • The PixInsight user interface         112
    • Working with images in PixInsight               114
    • Working with processes in PixInsight        117
    • Image and process containers      118
    • ScreenTransferFunction 118
  4. Layers and selections in Photoshop and Affinity Photo
    • Layers   120
    • Layer blending modes    121
    • Composite layers                 121
    • Working with filters non-destructively     122
    • Selections and feathering                123
  5. Fundamentals of pre-processing
    • Throwing out problem shots         124
    • The types of calibration frames   124
    • Pre-processing overview                  125
    • Creating master calibration frames             125
    • Dark scaling         125
    • Registration: aligning the calibrated subframes   127
    • Normalization   127
    • Integration methods        127
    • Bad pixel maps  129
    • The drizzle algorithm       129
  6. Pre-processing in PixInsight
    • WBPP or manual processing?       131
    • Before WBPP: Using CosmeticCorrection 131
    • Using WBPP: Loading and viewing files   132
    • WBPP: Parameters for bias, flats, and darks              134
    • WBPP: Parameters for lights          134
    • WBPP’s Calibration Panel                 136
    • WBPP’s Post-Calibration Panel    137
    • Presets  137
    • Running WBPP  138
    • Manual pre-processing in PixInsight          138
  7. Pre-processing in AstroPixelProcessor
    1. APP’s User Interface          142
    2. The files panel    142
    3. The image viewer panel                     143
    4. The pre-processing panel: Steps 1–6          144
    5. The TOOLS panel                 148
  8. Pre-processing in DeepSkyStacker             150
  9. Pre-processing in Affinity Photo    153
  10. Diagnosing common image problems
    • Misshapen Stars                   155
    • Diffraction patterns          157
    • Stray light              158
    • Halos     159
    • Flat fielding problems    159
    • Noise     160
  11. Principals and tools of post-processing
    • Types of processing tools                 162
    • Selective adjustments     162
    • PixInsight post-processing sequence         164
    • Photoshop/Affinity post-processing sequence      165
  12. Masks and PixelMath
    • Masks in PixInsight            166
    • Creating a luminance mask: clip and convolve      167
    • Creating a star mask with StarNet++          167
    • PixelMath              171
    • Using a uniform mask      173
    • Masks in Photoshop and Affinity Photo   173
    • Creating a star mask in Photoshop or Affinity Photo            174
  13. Color synthesis
    • Aligning color channel images in PixInsight            176
    • Aligning color channel images in Affinity Photo  176
    • Cropping out calibration artifacts                 177
    • Aligning histograms with LinearFit             177
    • RGB color synthesis in PixInsight                   178
    • RGB color synthesis in Affinity Photo         178
    • RGB color synthesis in Photoshop                 178
    • Narrowband mapped-color images             179
    • Bi-color HOO narrowband color synthesis                  180
    • Creating HaRGB images 181
    • Combining luminance and RGB data in PixInsight                  182
    • Combining luminance and RGB data in Photoshop or Affinity Photo              183
    • Blending RGB star data into a narrowband image                   183
    • Creating a synthetic luminance image      184
    • Combining color channels in AstroPixelProcessor                  184
  14. Color calibration
    • PixInsight’s PhotometricColorCalibration process                 185
    • Other calibration methods in PixInsight  186
    • The PreviewAggregator Script     188
    • Color calibration in AstroPixelProcessor 188
  15. Correcting gradients
    • Gradient removal in PixInsight    190
    • Gradient removal with AstroPixelProcessor             192
    • Gradient removal in Affinity Photo              193
    • Gradient removal in Photoshop  193
  16. Stretching the image
    • What is stretching?            197
    • Understanding the histogram      197
    • How different curves affect the histogram                198
    • Stretching in PixInsight 200
    • Stretching in AstroPixelProcessor                201
    • Stretching in Photoshop and Affinity Photo             203
    • Posterization: the perils of over-stretching               204
    • Stretching’s effect on color             205
  17. Noise reduction
    • Visual noise, color, and scale         206
    • Luminance masking for noise reduction 207
    • An introduction to scale-based processing                207
    • MultiscaleMedianTransform         209
    • TGVDenoise         211
    • One-step masking for TGVDenoise and MMT           212
    • ACDNR 213
    • MureDenoise      215
    • Desaturating the background      215
    • Noise reduction in Affinity Photo                  215
    • Noise reduction in Photoshop      216
  18. Adjusting color
    • Enhancing color saturation in PixInsight 217
    • Selecting Colors with PixInsight’s ColorMask script               217
    • SCNR      218
    • Enhancing color saturation in Photoshop and Affinity Photo            218
    • Balancing Color in Photoshop and Affinity Photo 220
    • AstroPixelProcessor’s HSL selective color tool       220
    • Narrowband color adjustment in Photoshop          220
    • Correcting magenta stars in PixInsight    220
    • Correcting magenta stars in Photoshop or Affinity Photo 221
  19. Contrast enhancement and sharpening
    • Creating contrast with S-curves  222
    • Contrast enhancement with the soft light blend mode       224
    • Local contrast enhancement in PixInsight                 225
    • Unsharp mask    227
    • Affinity Photo’s Clarity filter          229
    • The high pass filter            230
    • Dynamic range compression with HDRMultiscaleTransform             231
    • Deconvolution vs. sharpening     232
    • Deconvolution in PixInsight          233
  20. Star reduction and removal
    • Reducing star size               235
    • PixInsight’s MorphologicalTransformation              235
    • The minimum filter in Photoshop and Affinity Photo           238
    • Starless image processing with StarNet++                 238
    • Star reduction and removal in APP               241
    • Star removal in Photoshop             242
    • Reducing bright stars in Photoshop            243
    • Large halo correction in PixInsight              244
    • Large halo correction in Photoshop and Affinity Photo      245
  21. Cosmetic repairs
    • Cosmetic repairs in Photoshop and Affinity Photo                 247
    • Cosmetic repairs in PixInsight      248
  22. Plate solving
    • Plate solving       249
    • Image annotation               250
  23. Mosaics
    • Planning a mosiac              252
    • Mosaics in AstroPixelProcessor   252
    • Mosaics in PixInsight       253
    • PhotometricMosaic           255
  24. Image composition
    • Framing the scene              257
    • Color      260
    • Step away from the computer      261
    • Images and reality              261
  25. Example: Nebula workflow (starless)
    • Create the color image   262
    • Separate the stars and nebula      263
    • Process the starless image              263
    • Process the stars                   264
    • Recombine the images and apply final tweaks       264
  26. Example: LRGB galaxy workflow
    • Process the color image 266
    • Process the luminance image       267
    • Sharpen fine details and enhance contrast                268
    • Noise reduction and finishing touches     269
  27. Example: Star cluster workflow      270
  28. What are we looking at? [Digital bonus chapter]
    1. Nebulae                  273
    2. Star clusters         274
    3. Galaxies                  275
  29. Appendix A: Deriving the stack efficiency equation       276
  30. Appendix B: Deep-sky highlights  277
  31. Index  280
  32. Further reading         283

54 thoughts on “The Deep-sky Imaging Primer – Third Edition

  1. How to buy this book in India. From Amazon, shipping charges are more than the cost of the book.

  2. Hi Charles, I live in Canada and discovered that Amazon.ca doesn’t carry your book, which I thought was odd… anyway, is there anywhere in Canada that can source it for me (bricks-and-mortar or online)? – Rod

    1. Hi Rod –

      Sorry for the book not being listed on Amazon.ca. I can have a copy sent to you (media mail) for US$32. That takes 1-3 weeks. (Priority Mail is ridiculously expensive, but available for $47.) If you are interested, email me at deepskyprimer*AT*gmail.com. You may also check Amazon.com’s rates to ship a copy to you in Canada, as they may actually be able to ship it cheaper than I can.

      Thanks for your interest!
      Charlie

  3. Hi Charles,

    I’d like to thank you for your book! I’am french, I was trying to find a book about deep sky imaging but in french there are only 2 or 3 books that are dealing with astrophotography in general. Then I find your book on Amazon by chance. I looked inside and found it very good, with simple explanations… I bought it and I’m not disappointed! I had read the first part of your book and I find the answers to many questions… Thanks again! I’am going to read the next parts 🙂

    1. Thank you for your kind words about the book! I am happy to hear that the explanations are clear to you. I hope you enjoy reading the rest of it, and please send me a note if you have any thoughts or suggestions.

      Best wishes,
      Charlie

  4. Charles,
    You produced a wonderfully readable and information-rich book! I bought a copy about 4 months ago, and find I’m constantly referencing it for one thing or another. Yours is the first imaging book I’ve purchased, and I would eagerly recommend it to others. Excellent work!

  5. I think the book is great, however the font used is way too small. It is nice looking, but I have to make a real effort to read it. I would have much preferred a thicker book, but easy to read, after all books are meant to be read, not to be looked at. That is too bad, as the book deserves all the praises, and I do hope that a future edition considers this point of view. Thank you.

    1. Thank you for your helpful comment, Angelo. I am working on the second edition, and I have indeed increased the font size by one point. I’d rather have a thicker book too, but the book’s cost is based on the number of pages, so increasing the font size can increase the final price of the book. To balance the increased font size, I’m planning to increase the size of the book itself from 8×10 inches to 8.5×11 inches.

      Best wishes,
      Charlie

      1. Hello Charlie,

        Thank you for your reply. I understand your concerns and am glad to read there will be a second edition with an increased font size. Do you know when it will be out? Thank you.

        Best regards,
        Angelo

  6. Pingback: Academics - Page 2
  7. Have you considered releasing the book as an e-book? It’s great having a paper copy to read from cover to cover, but I find e-books much better for a quick reference. An e-book can go with me wherever I have my iPad. Eithe e-pub or pdf would be great.

      1. Hi Charlie, would like to buy both your Primer and The Astrophotography Sky Atlas. But I’m just interested in ebooks, for several reasons. I travel a lot, like to look back on stuff I have read, and then save shipping duration, cost – and environment. Unless truly forced – a principle. Many great hi-res tablets these days. No idea why you would choose iBook platform lock-in. Kindle is at least everywhere. ePub is great, can even accept (Adobe) DRM. If you do, please let me know, and don’t forget adaption to be within the readable! (this guy, like plenty of others, forgot to check: http://www.cloudynights.com/topic/507308-the-astrophotography-manual/)

      2. Thank you for the feedback. Now that the ePub and Kindle formats seem to be maturing, I will consider offering the second edition as an eBook. I’ve had several similar requests, and I completely understand the convenience of eBooks. I read most of my magazines now on the iPad. There are some challenges with the eBook formats that still make me hesitant due to the nature of my books: they are full-color with high resolution images. Neither book would be appropriate for monochromatic eReaders, as a lot of information is communicated with color in the figures, and one of the chapters is specifically about color. I fear the atlas is possibly too high resolution to work on an eReader. If I had a way to prevent those with monochrome devices from purchasing the books, I would be more comfortable. I don’t want anyone to be disappointed after downloading an expensive eBook!

        I still have a long way to go with the second edition though, so perhaps things will be different by the time I’m ready to publish it. Or perhaps I need to create a specific version for tablets that is designed for the format. I’ll investigate my options, and appreciate any additional thoughts you have.

        Best,
        Charlie

  8. Hi,
    I am hesitant to buy this first edition if the second edition is being released soon. What are the plans for the second edition, still looking for ab April release date?
    Thanks

    1. Sorry, work commitments have delayed my ability to finish the second edition. I do not expect to have it ready until later in the year now.

      Thanks,
      Charlie

    1. I’ve re-written sections 1 and 2 already, and I’m re-writing section 3 with a much greater focus on PixInsight this time. I have another book coming out next month (an astrophotography atlas), so work on that has delayed the second edition of this book. Thanks for your interest! When the second edition comes out will mostly depend on my work schedule, but I don’t think it will be ready before the end of this year.

      Best,
      Charlie

  9. Hi,
    I bought this about 18 months ago as a newbie. It’s one of the best you can buy on the subject. Covers most of the significant concepts in a relatively simple langauage that one can understand. Especially stuff like full well capacity, the coverage of the field of view and then processing tips as well. Well written with clean colour images. I still use it whenever I need to brush up. I bought several books before but this is the stand out for DSLR especially.

    Nalin

  10. Charles:
    I have the First Edition. I was working thru the exercises and came to Exercise 1.3 on page 33. The answer on p.185-186 confused me. How did you get 18.3 e- per second? From Ex 1.2, the thermal noise was 1.68e- per second at 20 deg C.
    Michael

    1. You are correct, this is an error in the book that carries over an old version of the question. The answer to 1.2 should read:
      “An exposure of 20 minutes at 40 degrees Celsius would produce 20 min x 60 sec x 1.68 e- per second = ~2014 electrons. Dark current would fill 2014 / 25500 = ~8% of the full well capacity. The brightest capturable level would be 25500 – 2014 = 23486. The noise from the dark current is SQRT(2014) = ~45 electrons. The read noise is given in the problem as 10 electrons, thus maximum theoretical dynamic range is 23486 / (45 + 10) = 428, or 53 dB.

      For the same exposure at -15C, following a similar set of calculations, the dynamic range would be 25468 / 15.6 = 1629, or 64 dB.

      (Note that we are simplifying our calculation of total noise here by not using the proper summing in quadrature method, as that is not covered until the following chapter, but this simplification does not have a meaningful impact on the results.)”

  11. Hi! I see there’s mention of a second edition of this book being prepared last year. Will that be released soon? I’d like to buy it.

    1. I took a year off from writing the second edition to create The Astrophotography Sky Atlas. Now I’m working on the second edition again, but it’s still a long way from done. Sorry for the delay. It can be hard to squeeze in the time to write with a full-time job and family!

  12. Hi from New Zealand. I wonder if your Astrophotography Star Atlas includes the Southern Hemisphere for all of us below the equator? I assume that you have probably spent most of your focus on only the Northern Hemisphere. thanks.

    1. Hi Larry – The atlas covers the entire Southern Hemisphere in the same detail as the Northern Hemisphere. With so many great objects visible from “down” there, I couldn’t leave out the southern skies!

      Best,
      Charlie

  13. Hi, I´m here to bug you, good Sir, for a digital version of your work. In my search for just that I see illegal downloadable copies in pdf-format out there. I simply refuse to go that way, it would not be fair to all that work you´ve put into your books.

    SO many people have a full colour tablet these days, I really think your work would reach more people that way. Pictures could be enlarged for potentially better viewing than on paper.

    E-books tend to come cheaper as well, no postage, no paper, instant delivery, has a lot of benefits. Please concider some sort of comercially available digital version of your work soon.

    For my personal interest, the Deep-Sky Imaging Primer is my first wish. I´m rather impatient when I see something I need for my hobbies. I´ll probably acquire the printed version none the less, while I wait for my wish to come true (around Christmas? 😉 ).

    Kind regards and hopes for clear skies
    Bjorn, Denmark

    1. Hi Bjorn – I appreciate your thoughtful note. As the e-reader market evolves (and I get feedback from potential readers like you), I am reconsidering my publication options. I still need to do some research on pricing structure, file formats (Kindle vs. ePub vs. iBooks), and resolution. All of my efforts right now are still on finishing the upcoming book, but once I’m done with that, I can see about releasing a digital version of The Deep Sky Imaging Primer.

      Best,
      Charlie

  14. Thanks, Charlie. And best of luck with your current work.
    I will order the hard copy asap. Can’t wait…

    To promote the digital version you could stress the practicality of having it along in dark conditions (if the book should find it’s use in real-time-next-to-scope situations, idk.), some ebook-apps have night lighting, so one doesn’t spoil night vision.

    I use both Blue Fire and iBooks, the former comes in both iOS and Android. Some inspiration: http://www.tomsguide.com/us/pictures-story/583-best-ereader-apps.html#s7

    Clear skies (and clear types)
    Bjorn

  15. Hi Charlie, minor copy error you’re probably already aware of. On page 171, figure 230 covers up the text. It’s not a critical error as the intent is clear in the image, but I wanted to make you aware of it. Stu

  16. I was wondering if your book shows information on filter wheels? I have two stellarvue refractors (80 & 105 triplets). What are the advantages of electronics over manual? Or is there any? I haven’t found anything that talks about filter wheels. Or what size filters are best 1-1/4” or 2”).
    Thanks in advance.

    1. Hi Stephen – Electronic filter wheels have enormous benefits. Mainly, it’s because you can set them to be controlled from your computer, allowing you to automate your imaging session with software like AstroPhotographyTool or Sequence Generator Pro. Otherwise, you’d have to sit by your scope all night and turn the filter wheel manually. Also, manual filter wheels won’t have the same accuracy in turning to the exact same spot, which is required for flat fielding.

      As for filter sizes, there isn’t a “best”–it depends on the sensor size, how close the filters are to it, and the focal ratio. For most APS-sized sensors, 1.25″ are okay for focal ratios slower than f/4. SBIG cameras of this size don’t put the filter as close the sensor, they usually use 36 mm filters. Larger sensors require 2″ filters.

      Hope that helps!
      Charlie

  17. Hello Charles, would it be possible to promote the information and image of the book in the next issue of the amateur astrophotography magazine please?

    Looking forward to your reply
    Steve

  18. Charles, I am enjoying your book. However, to get the most out of it you kind of need to be in front of the computer working through the examples you give. It would really be helpful if you could provide the images you use in your book to demonstrate PixInsight for download so that we could replicate your results as we work through the examples

    Thanks,

    Stuart

    1. Hi Stuart – I’m so glad to hear you are enjoying the book! The files used in the examples were several gigabytes in size, and I’m not sure I have them all at this point. Is there is a specific example you’d like to try? I can see if I can find the original data and send your way.

      Best,
      Charlie

  19. Hi Charles,

    Thanks for this very interesting book. I’m trying to work out the solution for ex 2.2 in the second edition. If my reasoning is correct then reworking the formula would yield a = 1.22 times wavelength devided by sin(1/206265). I do not get 173mm. Even using 173 mm in the formula itself and calculating the angular resolution does not yield 1/206265. What is wrong with my reasoning?

    Regards, Bart

    1. Hi Bart –
      I should have better explained in the text that the wavelength and aperture values are both in the same unit (meters). So the wavelength becomes 700 nm = 700*10^-9 meters. Your equation when you solve it should look something like:
      sin(1/206265) = 1.22 * 700*10^-9 / a
      with the value on the left in radians, it becomes
      4.848*10^-6 = 854*10^-9 / a
      a = 854*10^-9 / 4.848*10^-6
      a = ~0.176 meters = ~176mm

      Not only will I update the completed answer to show these steps better in the third edition, but I’ll also change Rayleigh’s criterion to drop the sin-1 function. I was being technically correct by including it, but for small angles, it doesn’t any material impact to the accuracy, so Rayleigh’s criterion just becomes resolution = 1.22 * wavelength/aperture. I think you’ll agree that equation is much easier to use! Reworking the problem with this approximation, it becomes:
      1/206265 = 1.22 * 700*10^-9 / a
      4.848*10^-6 = 854*10^-9 / a
      a = 854*10^-9 / 4.848*10^-6
      a = ~0.176 meters = ~176mm

      Thanks for bringing this to my attention.

      Clear skies,
      Charlie

  20. Hello Charlie;

    What is the chance that you will be issuing a revised edition again? PI has advanced quite a bit in the 4 years since your last update.

    Thank you!
    Ken

    1. Yes! I’m working on it now. Not only has PI advanced, APP and Affinity Photo have become a part of many people’s toolbox. I’m hoping to release the 3rd edition this fall to cover all of this.

  21. Hi Charlie, I can’t wait for your new edition;) Can you give us a more specific date? I am looking forward to hearing from you…Best regards from Switzerland;)

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