Tuesday, January 31, 2017

The Triumph of Science over science

February the 17th, 2017 marks the 417th anniversary of the death of Giordano Bruno. I know that many of my ardent readers are still trying to get over that.

Giordano Bruno's rather angelic looking Senior picture

Aristotle taught that the Earth is the center of the Universe. His proclamation cemented this idea into Western thought for almost 2,000 years. This is just one of the many examples of things that Aristotle said that mere observation would readily demonstrate to be just flat out wrong. Aristotle did lower-case science by decree. His attitude was that if reality disagrees with what he says, then reality is wrong.

Giordano Bruno challenged the idea of geocentricity (Earth being the center of all things) by proclaiming the heretical notion that the Earth travels around the Sun, rather than the other way around. He also proclaimed that the stars are just Suns like our own, but are just really darn far away. And (get this) Bruno said that those distant suns might have planets of their own, complete with living beings.

His challenge to conventional thought didn’t go over so well. He was burned at the stake by the Inquisition in 1600.

My attempts at marketing BBQ sauce have not proven successful

If Pew or Gallup were to do a poll asking people about Bruno, I’m gonna take a wild guess that most people would identify him as a pro wrestling promoter. Even if one were to restrict the poll to the scientifical and intellectual cream of the crop (which is to say, those people who regularly read my blog posts) I am gonna take another wild guess that a pretty small percentage would recognize the name Giordano Bruno. Yes, even the seven of you dear readers who have read more than one of my blogposts might say “who?”

But I should add that Bruno does have a crater on the Moon named after him. Kind of a small consolation what with his untimely death and all. I doubt if I ever get that honor. But if I do, I promise to look surprised.

Giordano Bruno, the lunar pimple

Some historians of science see Bruno as a martyr to the cause of Science. Perhaps he was killed for refusing to recant his beliefs about the universe?  But, perhaps not. I didn’t mention that he said quite a few nasty things about religion. More pointedly, he questioned some of the core beliefs of Christianity. The tamest of these was that the Bible is all about morals and stuff like that, and shouldn’t be treated like a textbook on astronomy. I’m not gonna get into all the other stuff that rankled the leaders of the church. Suffice it to say that his pontifications on religion were likely enough for the Inquisitors to get out their book of matches.

I think that explanation for his martyrdom is quite likely, but I’m going to make a different argument about why I don’t think Bruno was a martyr for Science. I argue that what he did wasn't Science. Bruno had some brilliant hypotheses that were way ahead of his time, but he didn’t do a lot of testing of those hypotheses. Testing of hypotheses is at the crux of Science. 


Bruno was not the first person to talk about the Earth revolving around the Sun. Artistarhcus of Samos proposed this in 270 BC. An astronomer from India by the name of Aryabhata claimed this around 400 AD. The first person in “modern” times to make such a claim was Nicholas of Cusa in the early 1400’s. This time period was the start of the Renaissance, when people started questioning the dogma that Aristotle had left us with. (Note the forming of a theme here concerning Artistotle.)

Show of hands… Who remembers Aristarchus or Aryvhata? Anyone? Who remembers sending out Nicholas-of-Cusa-Day cards? He was the guy who updated the Alfonsine astronomical tables? Yeah, I didn’t think you remembered him either.

This is not one of the Alfonsine Tables

How about another Nick… Nicolaus Copernicus? Ahhh… now I am seeing some name recognition. I think a lot of people who paid attention in Science class will at least vaguely remember the name. Something to do with the Solar System and planets and stuff? Yup. That’s the guy. A few people reading this may actually remember some self-proclaimed math guy who blogged about Copernicus.

Copernicus was a true Scientist, with a capital S. Aristotle and Giordano Bruno and Nicholas of Cusa? They were all scientists of the lower case variety. They were pontificators. They had an interest in Science, and pontificated about it. They had great intuition. With the exception of Aristotle, their intuition often proved correct. (Yet another subtle jab at Aristotle.)

But they weren’t capital S Scientists in that they didn’t follow the scientific method. They got the first part of the method: observe some junk and hypothesize about an explanation. Then they went forth and pontificated on their hypotheses. That might be lower case s science, but it’s not upper case S Science.

Copernicus took it to the next step. He also pondered on the possibility of a Solar System with the Sun at the center, but he went out and found data. In this case, it was largely data about the positions of the planets that was consolidated a zillion years ago by Ptolemy. Copernicus demonstrated in his posthumous book (On the Revolutions of the Heavenly Spheres, 1543) that “the Earth and the Planets travel around the Sun, and the Moon travels around the Earth” provided a simple explanation that fit the data.

This was how Science is supposed to work. It's all about data and hypothesis testing. When observations contradict a theory, the theory doesn't get all defensive and call the data a loser. The theory is rejected. And when a hypothesis arises that is simpler but provides as good of an explanation of the data, the older hypothesis is moved to the side. 

By the way, Copernicus also has his own crater on the Moon and one on Mars. Two heavenly spots for vacation homes.

Copernicus' summer home is the large complex in the center of the crater

As a side note… I have a big pile of files on my computer that contain books that I almost finished writing, one of which is a history of science. In order to find what I had previously written about Copernicus, I used a program to search my computer that is ironically named Copernic. True story. Good program, by the way.

A few more Scientists

It can also be said that Ptolemy (around 200 AD) did some Science. He started with a hypothesis, Aristotle’s geocentric universe, collected a lot of data, and found a mathematical explanation of the data. This is the way Science is supposed to work.

But much to the detriment of Western thought, Ptolemy went through gyrations (quite literally Spirographic gyrations) to describe the various motions in terms of Aristotle’s geocentric universe. He built an overly complicated model based on the assumption that Aristotle's tweets about the Universe were infallible, but I would still argue that Ptolemy was doing capital S Science, what with all the hypothesis testing and real data stuff.

Ptolemy's explanation of the course of the planets 

(I want to point something out here, just to make sure I haven’t been too subtle. Aristotle is the bad guy in this blog post. I also heard that he has small hands.)

Galileo also did capital S Science. You will likely remember Galileo for doing a bunch of stuff with pendulums and rolling balls down inclines. You might also remember that bit about when his press agent told everyone that he leaned over and dropped some balls onto a tower of pizzas. Don't always believe press agents! But I want to point out some Science of his that did not get as much press.

Galileo had heard of Copernicus’ work. He was taken by the idea of a heliocentric solar system. When he came upon the first telescope in 1609, he anxiously built one, and pointed it to the skies to look for evidence. He used the telescope to observe many things that the Roman Catholic church did not want to hear: the moon has craters (and was not perfect), the Sun had spots (and was not perfect), the planet Venus has phases (so it must rotate around the Sun), and Jupiter has bodies revolving around it (rather than all bodies revolving around the Earth). These ideas all went against the accepted doctrine of the time.

This was capital S Science, where observational data trumps hypotheses.

All great Scientists have beards. I have a beard. Draw your own false syllogisms.

And by golly, did the whole Inquisition crowd get ticked off when Galileo published Dialogue Concerning the Two Chief World Systems! Galileo wasn’t invited to a barbecue like Bruno was, but he was put under permanent house arrest. I am happy to report that the Catholic church quickly reversed this. It took them a mere 325 years to pardon Galileo.

Ironically, this guy who discovered the craters on the Moon -- Galileo -- doesn’t have a single crater named after him. All the rest of his gang got one. The injustice! All he got was "a large, dark surface feature" on Ganymede, one of Jupiter's moons. If ever there was an example of Stigler's law of eponymy, Galileo's craters are it.

Johannes Kepler is another guy who did capital S Science. He looked at data on the positions of Mars and deduced that the orbit of Mars around the Sun is elliptical. He also developed some laws regarding the speed thatplanets move around the Sun. Data and theory going hand-in-hand. Capital S Sceince.

Does Kepler have a lunar crater to call his own? Ya, you betcha. And the obligatory second one on Mars, and then gobs of other stuff in outer space.

How about Isaac Newton? No question about it, he did some capital S Science, in a large and bolded font. Newton took Kepler’s laws and had the Greatest Synthesis of All Science – he determined that Kepler’s laws were a consequence of the inverse square law of gravity, and vice versa. In other words, a simple rule about the relationship between distance and gravity replaced Ptolemy's Spirograph set as an explanation of how the celestial bodies move. And he invented calculus just to figger that out! Data begets a simple theory to explain a whole lotta stuff. Science don’t get no better’n that.

Newton got a crater on the Moon, and also one on Mars, just like Copernicus and Kepler. It's a shame though, that he didn't get a few asteroids and exo-planets. Newton doesn't even have is very own disambiguation page on Wikipedia like Kepler.

The triumph

This story has a happy ending. In the end, Science has triumphed over some smarty-pants guy who spouted off about a lot of bogus stuff that he just made up. Granted, it wasn't so happy along the way for some of the courageous people who challenged alternative facts with gosh darn real facts. But in the end, we wound up with Science that truly explains how the world really is. And there are no craters (that I know of) that are named after Aristotle.

Let us hope that we have the wisdom to let facts and data guide our course in the future.

Tuesday, January 24, 2017

The long, medium, and short of the cones

Color is three-dimensional. I've said that before. Almost four years ago, I blogged about how it is not possible to arrange all your crayons in a line. This led to a discussion about how you need three numbers to uniquely identify any color, because color is three dimensional. Hence, when we describe a color, we need three attributes.

In an RGB camera or on a computer monitor, those attributes are the intensity of red, green, and blue. In the Munsell color system, the attributes are hue, value, and chroma. In the CIELAB system, the three coordinates are L*, a*, and b*. In any color space, there are three.

Actual photomicrograph of the strawberry, lime, and blueberry cones in the eye

Why is color three-dimensional?  Simply put, it's because we have three types of color sensors (called cones) in our eye.

In case this is starting to sound familiar, I have talked about the three sensors before. I blogged about how having three color sensors can lead to something called metamerism, where two objects can have identical colors under one light, but look different under another. I have blogged about colorblindness which is caused by missing one or more of the three cones. This came out in a blog about apps for testing for colorblindness, And then a followup blog post about colorblindness, and in one which asked the metaphysical question about whether two people see color the same way.

But today, I want to talk more about what those three cones look like.

Rainbowology 101

Time to pound some Fezziks into your head

Below is an artist's rendition of a rainbow. I like saying that my drawings are artist's renditions cuz it makes me feel like an artist. But perhaps it would be better if I call this a scientist's rendition, since I did actually put a little effort into making it anatomically correct. I am referring to the spacing and positions of the colors and the numbers on the scale below the rainbow.

The scale at the bottom is in wavelength and is measured in nanometers (abbreviated nm). A nanometer is a really tiny unit of measurement ... like about the width of a dent in a hair on a freckle on the butt of a baby flea that is the runt of the litter. A nanometer is the distance I will move over in the middle of the night when my wife tells me I'm hogging the bed. There is a whole lotta Fezziks behind wavelength and nanometers and how they got involved with rainbowology, but that would be getting off the topic. For our purposes, a nanometer refers to a position in the rainbow. At one end (400 nm) light is violet, and at the other end (700 nm) it's red.

If I wanted to be pedantic, I might extend the rainbow a bit. We can see light, however faintly, as low as 380 nm, and all the way up to 780 nm. So, I am lying when I say that my rainbow is anatomically correct. But it is a useful lie.

Strawberry, lime, and blueberry?

The obvious first guess is that there must be one set of cones in the eye that respond to the red part of the spectrum, one set that respond to the green part of the spectrum, and one set that respond to the blue part of the spectrum. Go RGB! 

Let's assume that the blue cones respond to light that is between 400 nm and 500 nm, the green cones respond to light that is between 500 nm and 600 nm, and the red cones respond to light between 600 nm and 700 nm. The top half of the picture below shows a graph of the sensitivity of each of the three cones as a function of position in the rainbow. Below that, we see the hypothetical rainbow that such an eye would see.

First guess at the response of the cones.

I don't know what you see when you look at a rainbow, but my rainbow has more that three colors. So, saying that the three cones respond each to their own 100 nm wide part of the rainbow is not just a lie. It's a lie that isn't even useful. The worst kind, if you ask me.

One of the difficulties with the first guess model is that it has the cones responding equally to all wavelengths within their respective ranges. That is why the first guess rainbow looks so blocky, and to be honest, very few light sensors in the real world have such a flat response.

So, let's tweak our hypothesis a bit. The graph below shows a second guess at sensitivity of the three hypothetical cones in the eye. So, as before, the blue cones will collect light that is in the range from 400 nm to 500 nm, but they are less sensitive near the ends of the ranges.

Second guess at the response of the cones

Note that the hypothetical rainbow has a decidedly more natural look, but it still doesn't look like a rainbow. I like my rainbows (and my brandies) with a little splash of orange. And then there's the dark areas. I don't ever recall seeing black listed as one of the colors of the rainbow.

Strawberry, strawberryish-lime, lime, limish-blueberry, and blueberry?

You know when you get one of those triple scoop cones? The fun part is when you are transitioning from one ice cream to another. You get a bite with some strawberry and some lime. You're not sure how much of each will be in the bite, and you're not sure how peacefully the two flavors will coexist in your mouth. But it will be fun. 

We can try that with our hypothetical cones... mush together the responses of the strawberry with the lime, and the lime with the blueberry. In this third guess, the responses of the cones have a significant overlap. So, if light at 500 nm comes in, both the green and the blue cones stand up and proudly wave their little neurons to say that they see the light.

Third guess at the response of the cones

I think that this has enough of the rainbow vibe to get Kermit the Frog to reach for his banjo. But when it comes to anatomical details, I think we can do a little better. Note that the yellow in the third guess rainbow is at 600 nm, when in reality, it's zip code is pretty close to 570 nm under cool lighting and 580 nm under warm lighting. Sky blue is another color that doesn't quite land in the right spot. I would really like for it to slide down from 510 nm to maybe 470 or 480 nm.

Based on that, I adjusted the width and position of the three hypothetical cone responses. Here is what I come up with - my final guess at the spectral sensitivity of the three cones in the human eye. Note that this analysis is pretty rudimentary. This was just a Gedanken - thought experiment. No lab rats were inconvenienced by the experiments described herein.

My fourth and final guess

The real answer

How close did I come? This last image shows one reliable estimate of the response of the three cones.

A guess from some real experts

I am rather pleased with my guess. I did of course, have the benefit of knowing what the real response looked like, and all the time in the world to rationalize my own estimate. But, I think the point has been made that the response of the three cones in the eye is not as simple as red-green-blue.

In fact, the responses of the cones really aren't red, green, and blue. There was a movement to call them by the Greek letters rho, gamma, and beta. Clever... you know? But the official designation is now to call them L, M, and S cones. L stands for long, or long wavelength, and it is the curve that is furthest to the right - the one we would be tempted to call red. M stands for medium, and it is the one in the middle. I still kinda think of it as green. And S is the short wavelength cone, the one that is furthest to the left. Speak kindly to it. It's kinda blue.


Why do I bother with all this explanation? First off, just cuz it's fascinating. Anything to do with color is gosh-darn interesting.

But this overlap between the L and M cones is kind of a head-scratcher. In those brief moments when I think like an engineer, I often think about stuff like how reducing the correlation between sensory channels increases the entropy of the system - the efficiency of information gathering. Based on that, I would think that the engineers who designed the human eye would have avoided overlap, especially such an egregious overlap.

But while Dr. Eva Lution (the designer of the human eye) doesn't always come up with the best designs, the poor designs are mercilessly discarded. I am left with the conclusion that maximizing entropy might not be the only worthwhile goal.

Note that as we slowly move upward in the rainbow from green to red, the response from the M cones is decreasing while the response from the L cones increases. This has the effect of accentuating the change, since the human visual system relies on comparison of L and M to discern greenish to bluish. Thus we see very rapid change, with green, yellow-green, yellow, orange, reddish-orange, and red all packed into 70 nm. If you are a photon out to have a wild time, this is where the action is.

There was one blogpost of mine about why we evolved to have three different colors sensors. I argued in this post that the addition of the L cones allowed us to see the difference in leaves as they change color. The additional cone also makes our eyes sensitive to a change in hemoglobin at the surface of the skin. This has some clear advantages for a social animal who does not have fur on its face. (With the exception of color scientists, who have beards and have yet to evolve into anything useful.)

Oh... what a little L cone can do

And that, dear reader, is why the L and M cones have such flagrant overlap.

Wednesday, January 18, 2017

Comparison of inexpensive digital microscopes, part 3

I promised that my review of inexpensive digital microscopes would be a trilogy, and by golly, that's what it's gonna be. In part 1, I looked at the Celestron USB microscope. In part 2, I had a quick peek at a lens that turns your smart phone into a microscope. In this blog post, the third part of the series, I look at a microscope that I just purchased from Opti-TekScope. It sells for $89.

The Opti-Tekscope in the stand (left), and frees ranging (right)

I think this microscope is the greatest thing since the invention of the microwave DVD player. (I watched all 53 episodes of Downton Abbey in 37 minutes.) The microscope gives me very nice images at a resolution smaller than my two previous microscopes, and the stand is solid. 

If I can interject a techno-linguistic question for the moment, I have wondered about the proper terminology when you compare the resolution of two microscopes or images. I think it is common to say "higher resolution" when you refer to an image that has a higher magnification. But technically, resolution refers to the tiniest discernible feature. I could speak of being able to make out a dot that's 10 microns in one image and 100 microns in a second image. In common terminology, we would refer to the first image as having higher resolution, but that runs counter to the size of the numbers.

This is the kinda stuff that keeps me up at night.


You get a new camera, what's the first thing you do with it? Here is a series of selfies that I took with this microscope. I think this is pretty impressive. I mean the images. Of course my beard is pretty impressive. I can almost use this as a webcam, and alternately, I can also tell whether my barber did a decent job trimming an individual hair of my beard.

Proof that I still have brown hairs in my beard
The eyes have it

Below I show a comparison of an image from the three microscopes I have looked at so far. How to characterize them???

Subjectively, I would say that the three images have similar resolution. The Opti-TekScope image on the far right has a slightly reddish cast - the magenta dots seem more predominant. The Celestron image on the far left looks a bit washed out. But overall? I wouldn't complain a whole lot about any of them.

Except if I started getting picky. As I said in my last blog, the image at the far left is not just washed out, but also a bit blurrier than the one in the center. But take a real close look at the image from the cell phone. Look on the left edge of the eyebrow. (See the circled area in the cropped image below.) There are some white splotches in there that look very suspicious. You don't see those white splotches in either of the other images. For the time being, I am going to explain these as artifacts in my cell phone camera. Yet another thing for me to investigate. That's gonna keep me up at night.

Are these white splotches spies on a covert mission?

But there's more... The aforementioned comparative study of the model's conjunctiva did not take full advantage of the Opti-TekScope. It's barely warmed up! How about this image comparison?

Now we got a gosh darn good image of the nevus!

It is clear from this set of images that the resolution of the Opti-TekScope is way more better than the other two. It would be ok to use the other two images to measure the size of the halftone dots, but you can truly see the details inside of the halftone dots with the OptiTeckScope.

Pixels on my KindleFire

In the previous two reviews, I had a look at Wikipedia. Not the website; the icon. I looked at the Wikipedia icon on my KindleFire. As you may recall, the Celestron gave me a usable image of the pixels in the display, but the cell phone microscope was unable to focus properly. How about a side-by-side image of the Celestron and Opti-TekScope? I think it's clear that the Celestron image is blurrier.

Which photomicrograph of a Wikipedia logo would you invite to a Starbucks date?

You may be wondering... Why do I point a microscope at a display? Teaching. I want to teach the idea that practically all the displays we look at (TVs, computer monitors, cell phones, laptops, and tablets) are made up of three colors of dots. All the colors that we see when watching a microwave DVD version of Downton Abbey are created by mixing the light from red, green, and blue pixels. I have given the "let's look at the pixels in a computer screen" demo in color classes about eleventy-seven times. (Sounds like something good for a blog post or two.) I think I finally have a good way to demonstrate the effect.

I think this clearly demonstrates that the resolution of the Opti-TekScope is more better than the Celestron.

The last stand

Finally we come down to what holds the whole thing up. If you recall the Celestron microscope, it has a stand that is adjusted via the articulation of three ball-and-socket type joints. I was not happy with it. In fact, at 3:00 AM this morning, when I finished obsessing over the correct meaning of the adjective higher in phrase higher resolution, I decided to start fuming about how hard it was to position the Celestron. Whatever. It was a good reason to get up an raid the fridge.

But the stand that comes with the Opti-TekScope works just like I would hope a simple microscope stand would work. It moves up and down, without messing up the direction the scope is pointing. By much. Focus is adjusted with a knob on top. The knob is gentle enough to not spoil the pointing of the scope. By much. 

I'm not going to claim that the stand is a work of art, or that it looks like it would withstand a nuclear detonation at 50 feet. That part I didn't test. But the stand is quite functional.

I have looked at three microscopes so far. Of the three I have played with, this one, the Opti-TekScope is by far my favorite. Come to think of it, it is also the most expensive. But for $90... I think it's a good deal. You should buy one for all your grandkids.

Thursday, January 12, 2017

Comparison of inexpensive digital microscopes, part 2

In the previous blog post, I reviewed one popular USB microscope, an inexpensive one from Celestron, which can be had for about $40. Not a bad price, you say? Well, have I got a deal for you! How does $7.50 sound? Note the decimal point... Yes, I can get you behind the wheel of a digital microscope for less than the price of a hot date at Starbucks.  

I found this little baby at one of my favorite geek-stores, American Science and Surplus. I am lucky enough to live in Milwaukee, one of but a few cities that has a brick and mortar store. But this particular item I ordered online. Note the really alluring name: "95231P1 PHONE PHOTO LENS MICROSCOPE". 

A loupe for your cellphone

As you can see in the photo above, the device is not a USB camera at all, but a lens and illuminator that snaps onto your cell phone. Hence the really low price. It leverages Apple's team of 800 engineers who worked on the camera in the iPhone, and takes advantage the fact that you already spent a bunch of money cuz you just had to have the latest iPhone. Another secret to the low cost is (no doubt) their tight marketing budget for naming the gadget.

Seriously, the little gadget is convenient cuz it uses my cell phone's autofocus, the user interface is the same as my cell phone, and my granddaughter can teach me how to get the images I take onto my computer.

I took an image of a model's eye with the Celestron camera in the last blog post. Below is a quite serviceable image of those same halftone dots taken with my Phone Photo Lens Microscope. My granddaughter was able to help me out, of course.  

I am but a halftone dot in the model's eye

Just in case you were too lazy to read the previous post, I have assembled a side-by-side comparison of the images taken with the two microscopes. I should mention, I did not rely on the 800 engineers who designed the iPhone camera just to make my selfies look fabulous. I relied on the guy in his basement with a soldering iron who developed the camera in my Samsung. He did just as good a job. He just didn't have a good publicist.

My first impression is that the cell phone image is more better. The colors on the image from the Celestron (at left) are a bit washed out. This could be a veiling glare problem, but I did clean the Celestron lens as best as I could. Another thing of note -- the yellow halftone dots are far more discernible in the cell phone image (at right) than in the Celestron image. 

Below, we see a zoomed version of the white of the eye of the model - same digital images, but with a little digital jiggery-pokery. I also did a little enhancement of the brightness and contrast of the Celestron image in order to more fairly compare the resolution. Note the tiny little black halftone dot that can be seen in both images. If I had to make a call, I would say that the cellphone image gives a better rendition. In other words, the cell phone microscope has higher resolution than the Celestron.
At this magnification, the original sexiness of the model's eye has significantly diminished

What's the magnification?

I am gonna take a wild guess here. I am gonna guess that a fair share of the folks who read the first blog post in the series and are this far along in this blog post have been wondering about the magnifications of the two microscopes. I have intentionally left that little tidbit out, since it is not quite as relevant as one might think. Permit me a moment to enter the didactic mode of discourse.

Original definition of magnification

The image below illustrates the concept of magnification as it originally was applied to a system with a bunch of lenses. Only one lens is shown below (because I am lazy), but the concept applies equally well to a a combination of a bunch of simple lenses that constitute what we cleverly call a lens, as in camera lens. Yes, a lens (such as you buy at the camera shop) is made up of multiples lenses. I love the English language. This makes it great fun to write patents. 

Lenses can be used to focus arrows - important for deer hunters

In the depiction above, the object is the arrow at the far right of the picture. The lens images this arrow to the other arrow at the right right of the picture. This arrow at the far left is called the image. This is not to be confused with the digital file that comes out of your camera, which is called an image. This makes it great fun to write patents. Henceforth, I will try to remember to use the term digital image to refer to a digital file which is a representation of an object.

The magnification of this configuration is simply the ratio of the size of the two arrows. In this case, the magnification is 2X. The image of the arrow is twice the size of the original arrow.

A second definition

The previous definition of magnification works well for a microscope where you look through an eyepiece, or for those ancient pieces of technology that were called film cameras. Enter the digital camera. The object is now imaged on a CMOS sensor which might be a five millimeters across. If my microscope projects an image onto the sensor of an object that is four millimeters across (such as the first depiction of the model's eye), then the magnification of the lens is 0.80X. Wow. Doesn't sound like such good marketing to say that a microscope has a magnification of less than 1X! I think that even a company that can't afford to pay for a decent name would eschew publishing such a spec.

Not only is it bad marketing, but it is a downright useless as a spec. I will never view the digital image at a size of a few millimeters. That digital image might be magnified to fit my cell phone, which is 110 mm across. In this case, the effective magnification is around 110/4 = 27.5X. Then again, I might view that digital image on my computer monitor which is 480 mm across. The magnification is now 120X. Or, of course, I could zoom in on the digital image as in the illustration where the field of view is big enough to capture five halftone dots across. I could make that into a billboard, and get a magnification of a gazillion X. Or, I could set up a high power projector to project the digital image onto the moon and be able to say that the magnification is a gazilliontillion.

Microscope with high mag wheels

But, the Celestron microscope mentioned in the previous blog has a spec of 150X. What does that mean? Their spec is base don blowing up the image to full screen size on some monitor. Whether the monitor is a 14" or a 36" monitor is unknown, at least from the Amazon website. This is a useless spec. (I should point out that the Celestron webpage for this model gives a complete (and hence useful) spec. They say the microscope is 150X on a 19" monitor. 

I think you see my point that magnification is kind of a meaningless spec without qualifying the spec by saying what size display is to be used and how the digital image was zoomed.

A third definition

There is a third definition of a quantity that relates to the power of a digital microscope which I kinda like. It's simple to calculate, even for the layman, and it is more useful than the X number: object pixel size. You simply determine the size of a pixel.

As an example, we look at the first digital image of halftones in this blog post, the one captioned "I am but a halftone dot in the model's eye". The field of view is about 4 mm horizontally. I look at the digital image of that on my computer, and find that my cell phone gave me an image that is about 4,000 pixels wide. The object pixel size is thus 4 mm / 4,000 = 1 micron. This is the highest magnification available with this lens and my cell phone. 

(I measured  the catalog page with a ruler to determine the 4 mm wide field of view. If your measurement is critical, I would suggest buying a thin ruler and placing that in the field of view for at least one of the pictures. Note that until you refocus the microscope, the pixel size of the object will be the same - if the object is still in focus.)

As a second example, we look at the Celestron microscope that was reviewed in that spectacular blog post that preceded this one. This is a 1.3 MP camera, which means that the entire field of view is 1.3 million pixels. So, the horizontal pixel count is around 1,000. When this microscope is adjusted so as to have a field of view that is 4 mm wide, then the object pixel size is around 4 microns. Of course the Celestron can go higher in magnification by moving the camera. I figger the tiniest object pixel size (highest magnification) of that Celestron microscope is about 1 micron.

This is image is four mega pickles

Based strictly on that number - minimum object pixel size, the effective magnification of the two microscopes is pretty similar.

A third definition

But that still doesn't tell the whole story. In the side-by-side comparison of the little black halftone dot in the white of the model's eye, I made the call that "the cell phone microscope has higher resolution than the Celestron". This is an incorrect statement, if we define resolution as the object pixel size. But resolution is a fuzzy thing. Or, to be literal, resolution is the opposite of fuzzy. Resolution means that the image is "sharp". And sharpness is a fuzzy thing to measure.

If I were a real scientist, and not just someone who plays a scientist in the blogosphere, I would start talking about using "resolution targets to determine the modulation transfer function". In simple terms, you point your microscope at a test target with finer and finer sets of lines. When you can no longer see (resolve) the lines, then your microscope has run out steam.

Everybody needs one of these in their wallet, by golly!

But alas... the test target sells for more money than the microscopes that I am looking at. My dear readers will have to settle for a picture that is worth 1K words.

The second test

I almost forgot about the second test that I did with the Celestron microscope, which was looking at the pixels of my Kindle display. Speaking of fuzziness and resolution...

Fuzzy Wiki was a bear...

This is an excellent example of an image with object pixel size that goes way beyond the inherent resolution in the image. Basically, no matter how hard I pleaded with my cell phone, I could not get it to focus on the Kindle pixels. There will be no discerning of red, green, and blue pixels in Mudville tonight.

Note, for this microscope to work, you need to set the lens atop of whatever you are looking at. On the plus side, this makes it easy to position the microscope. On the minus side, this makes it impossible to adjust to a different working distance. What you see is what you get.


The Phone Photo Lens Microscope is downright cheap. It's a bargain if you are in interested in a handy tool for looking at the quality of print, and documenting that. But it is a really a fixed focus device. Aside from the digital zoom of your cell phone, you have little control over the magnification of this puppy. But it's downright cheap. The image quality is good. And I should also mention that it is cheap.

I know there are other cell phone loupes on the market. I don't know if they work as well as this does. But I know you can get this one at American Science and Surplus. Buy one quick... I'm sure they will go outa stock as soon as this blog hits.


So far, I have not received money from either Celestron or from American Science and Surplus in exchange for my reviews. Not that a little kickback wouldn't be appreciated. My granddaughters are starting to think about college. I'm just saying...