What is the Ecliptic? — Sky & Telescope, September 2022 — Errata

The inaugural Sky & Telescope article of Beginner’s Space – What is the Ecliptic? already has a serious error: the Earth is drawn incorrectly! Even in this artful depiction, it’s clear that the orientation of the continents should be rotated clockwise by 23.4°.

In the equatorial-azimuthal projection used there, the Geographic North Pole of the Earth (which of course projects to the North celestial pole) should emanate from above central Canada, not from above eastern Canada, as drawn in the article. Similarly, the Celestial equator (not the Ecliptic) should be drawn as the projection of the Earth’s equator (as correctly described in the article), which of course runs across the top of South America.

Let’s hope not too many new readers are confused!

agc

Image Stacking — Sky & Telescope, April 2022 — Errata

The following errata correct the April 2022 Sky & Telescope Article, Image Stacking Demystified, by Richard S. Wright, Jr.

  1. The cumulative image noise is proportional to the square root of the number of frames being stacked.
  2. Mathematically, the shot noise from the imager and associated electronics can be considered to be added to the signal.
  3. The horizontal axis in both graphs on p.56 should be labeled “number of stacked frames,” and the vertical axis should be labeled “quantity.”

EXPLANATION

1.  The S&T author writes, “Shot noise is also quantifiable — it’s simply the square root of the signal value.” This is incorrect, as are the numerical examples that follow the statement.1 The noise and signal components are separate entities, and one cannot say that one of them is a function (square root) of the other.  (Actually, some systems do have an interaction between the two, but those are usually 2nd-order, minor effects, and are not relevant in the image stacking situation.)  The noise value is completely determined by the physics of the imaging device and the transistors in the related electronics, and is independent of the signal – it’s even there when there is no signal (e.g., a dark frame).  The incorrect statement would imply that a dark frame has zero noise, which is not true: in addition to fixed pattern noise (which we can reduce by subtracting a dark frame when doing advanced image processing), the dark frame will have its own random noise, too.

What is really happening is the following.  When we stack multiple images, we are literally adding the images together, pixel-by-pixel.  That means that the signal components get added together, and so do the noise components.  When the images are properly aligned (registered), the signal components at each pixel from one frame to the next add together as correlated data, since they are part of the same image. This combination is literally a simple addition, so image stacking increases the signal component in proportion to the number of frames being stacked.

However, the noise component at each pixel from frame to frame is uncorrelated, because it is a random process.  The noise components add together as orthogonal vectors, which means that the noise value increases by the square root of the number of frames being added together.  (The stacked images are then re-scaled, so that the resulting image doesn’t get progressively brighter everywhere – but this, of course, scales the noise by the same amount.)  The signal-to-noise ratio improvement is therefore proportional to the square-root of the number of frames that are stacked.

2.  The S&T author writes, “It’s important to bear in mind that this noise is not something that gets added so much as something that’s missing.” This is incorrect.  The mathematical modelling and analysis of signals with noise accounts for each of these elements as an added component; there is nothing “missing” from the original signal, which still exists in the image capture.  In practice, this can be readily seen by using a spectrum analyzer, which will show that the signal and noise are separate components.  The shot noise from the imager and associated electronics should be considered to be added to the signal.

3.  The graphs on p.56 are labeled incorrectly. The horizontal axis in both graphs should be labeled “number of stacked frames,” and the vertical axis should be labeled “quantity,” as it represents either signal or noise in the left-hand graph, and signal-to-noise ratio in the right-hand graph.

—agc


FOOTNOTE (1):

There is a different quantity, known as photon noise, which is characterized as the square root of the photon signal, but this is not the dominant factor in our calculation of signal-to-noise ratio, because we are considering the net effect over a set of stacked frames.


REFERENCES:

Wikipedia: Shot Noise – note the discussion regarding “square root of the expected number of events.”

Wikipedia: Gaussian Noise – “values at any pair of times are identically distributed and statistically independent (and hence uncorrelated).”

Philippe Cattin, Image Restoration: Introduction to Signal and Image Processing.

Robert Fisher, et al, Image Synthesis — Noise Generation.

 

 

Transit of Mercury – Live!

There will be a rare astronomical event this Monday, November 11, 2019, when Mercury passes in front of the sun. We’ll be streaming it live from NJ using a telescope. The event occurs only about 13 times a century.

Click on the player to see the live stream during the event!  We’ll also stream the end, at 1:00pm EST, and on the quarter-hour in between, as well.  Weather permitting!

transit of Mercury
Transit at 11:47am EST

Technical information

  • Questar 3.5 Cassegrain-Maksutov telescope with chromium solar filter
  • Lumix GH2 camera, 1080p24 source video
  • KanexPro HDMI/3G-SDI converter
  • Haivision Makito X video encoder /streamer, down-converted to 720p
  • HLS playback on HTML5 with Flash fallback for older browsers

Special thanks to …

  • John Turner, Turner Engineering − encoder, technical support
  • Wowza Media Systems − Wowza Streaming Cloud
  • Cathy McLaughlin − location support
  • Charlotte Cugnini – production assistance
  • Lizzie Cugnini – production assistance

Solar Eclipse Wows Tens of Thousands in Madras, OR

Bowing to the awesome spectacle that is a solar eclipse, this observer, together with his extended family and countless thousands of other umbraphiles, witnessed the awe-inspiring beauty that is this rare natural event. Despite the wildfires raging nearby, we were treated to near-perfect sky conditions in the high desert surrounding Madras, OR, a normally-modest town of just over 6,000 residents — which blossomed to possibly 30,000 or more in the days preceding the August 21 event.

Fires raging, north of Madras, OR

As the partial phases progressed, the crowd delighted in witnessing the transformation of the environment into an alien, bizarre landscape.  Shadows took on new, unfamiliar characteristics, with even one’s own fingers creating pinhole images of the the crescent sun.

Close-up shots showed the moon’s silhouette encroaching on a sunspot-adorned image of the sun’s disc.

Moon encroaching on the sun, Questar 3.5 w/ 100mm focal reducer

Then, finally, amid cheers from the crowd, the pièce de résistance.

Total eclipse at Madras, OR, 10:20:35 AM PDT

While photographic techniques have evolved vastly in the past few decades, nothing can truly portray the personal experience at such an event.  To anyone who has seen a total eclipse, it is obvious that the difference between “99%” and “100%” is orders of magnitude greater than the mathematical “1%.”

Nonetheless, here is an attempt to capture the timeline of the event.  Allowing for artistic license, this picture combines different views of the eclipse, taken from the SolarFest “Solartown” campground.

Time-lapse sequence/montage of solar eclipse and Mt. Jefferson (in shadow), at Madras, OR

To some, the two minutes and five seconds of totality – replete with a 360° sunset-like horizon – lasted a lifetime; to others, it was over in a brief instant.  But even a novice could capture what could be a once-in-a-lifetime record of the event.

Eclipse shot by Sammi Dehen, Canon camera w/ 50mm lens

And then, it was all over.  (For a 15x time-lapse video of the shadow approaching and passing by, click here.) The die-hards remained in place until the last moments of exiting partial phase, while the novices departed seconds after totality ended.  Even the normally-quiet VFR-only S33 Madras municipal airport – which brought in a mobile control tower to handle the increased traffic – suddenly roared to life as opportune aristocrats jetted out from their brief two-hour stay.

Cugnini family (et al) at the levee, Solartown campground, Madras
Dehen family at the eclipse

This was the second total eclipse that I have witnessed (the first in Cabo San Lucas, Mexico, 1991), and both times, I was struck by the humbling experience of an earth – and solar system, and universe – of which we are such a small, but influential part. Nature and physics plod on, despite our meddling interference; may we be wise (and generous) enough to be a constructive part of this grand scheme.

— Aldo Cugnini

Photo credits: Aldo Cugnini, Charlotte Cugnini, Elizabeth Cugnini, Sam Dehen.

The Wrong Kind of Special Interest Group

Is Amateur Astronomy Headed Towards the Top 0.1%?

THE CURRENT ELECTION CYCLE – theatrics aside – brings up a point of great concern to many voters:  the top 1/10th of 1 percent in America owns almost as much wealth as the bottom 90 percent.  I can’t help but wonder if amateur astronomy is headed in this same, disturbing, direction.

For the first time in many years, I decided not to attend a well-known and highly-promoted astronomy expo on the East Coast, as it had become, I believe, prohibitively expensive. In the past 15 years, the entrance fee has soared from $10 to $25, a yearly increase of more than 6%.  To say “soared” is not an exaggeration: compare that increase with yearly inflation, which has largely been much less than 4% over the same period, and sometimes even negative.

Looked at another way, the door price at this event has increased 2.5 times, while consumer prices have only gone up 1.3 times over the same time span.  I am reminded of the case years ago of a 12-year-old boy’s complaint of a price increase made by a well-known model paint company, which actually spurred government intervention – but I digress.

Other hobbies, by comparison, seem to have more reasonable event pricing: the yearly ham radio convention is $20 (for advance sales), the largest RC aircraft model show is $15, the biggest model railroad show is $13, and the largest photography show is free to attend exhibits.  (There are similarly some very large professional conventions that have free admission, only charging for attending lectures.) And all of these other hobbies have entry-level products of good quality and low cost, to boot.

The bigger concern is that this kind of pricing, even with student discounts, makes the exposition inaccessible to many families seriously considering the activity.

When a year’s membership in a local astronomy club can cost considerably less, this level of event pricing is not in sync with the budgets of lower- and middle-income families, especially for a pursuit that should be aiming to increase public accessibility and participation.  Worse, for a highly-publicized event, there is the impression of an elitist hobby, especially given the many exhibitors that display equipment running into the tens of thousands of dollars.

Not surprisingly, a well-known astronomy magazine declined my request to publish this opinion piece, disagreeing with my position, and also citing a business relationship with the producer of the astro expo (who did not respond to my posting on their Facebook page).  At the same time, a former official of the expo completely agreed with my remarks, saying that the pricing was “totally out of control,” and motivated by financial gain.

My own love of astronomy began as a child, when my dad bought me a very low-cost (and somewhat wobbly) reflecting telescope made by the A. C. Gilbert Company.  While no one endorses the need for more low-end telescopes of mediocre quality – department stores continue to be rife with them – the call for affordable and suitable entry-level scopes like the original Edmund Astroscan seems to have all but vanished.

Expo promoters should consider alternate pricing schemes that will attract newcomers, such as different entrance pricing without the talks, discounts for advance admission, or other similar reductions.  Astronomy, equipment, and consumer-facing events must be made accessible to a broad range of the public, and never give the impression of exclusivity. It is an obligation that companies and event promoters owe to all of the public, not just the top few percent.

Aldo Cugnini is a video technology consultant and lifelong amateur astronomer. He writes for a number of professional trade publications and dabbles in RC helicopters and ham radio.

CARTOON © COPYRIGHT 2011 BILL SCHORR – USED WITH PERMISSION.