How To Be Using Point Spread
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How To Be Using Point Spread
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As the world's only manufacturer of light, X-ray and electron/ion microscopes, ZEISS offers tailor-made microscope systems for 3D imaging in biomedical research, life sciences and healthcare. A well-trained sales force, an extensive support infrastructure and a responsive service team enable customers to use their ZEISS microscopes to their full potential.
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In this article, we’ll talk you through the Point Spread Function.
Suppose that you have a tiny fluorescent object, such as a 10 nm-diameter fluorescent bead or even a single fluorescent molecule, and you try to observe it under a fluorescence microscope.
Provided that the object is bright enough, even though it is well below the resolution limit of your microscope you can still see the object, but it will appear larger than it really is.
Diffraction of light, which determines the microscope’s resolution limit, blurs out any point-like object to a certain minimal size and shape called the Point Spread Function (PSF).
The PSF, then, is the three-dimensional image of a point-like object under the microscope.
The PSF is usually taller than it is wide (like an American football standing on its tip) because optical microscopes have a worse resolution in the depth direction than in the lateral direction.
The PSF varies depending on the wavelength of the light you are viewing: shorter wavelengths of light (such as blue light, 450 nm) result in a smaller PSF, while longer wavelengths (such as red light, 650 nm) result in a larger PSF and, therefore, worse resolution.
Also, the Numerical Aperture (NA) of the objective lens that you use affects the size and shape of the PSF.
A high-NA objective gives you a nice small PSF and, therefore, better resolution, as demonstrated in Figure 1 (an interactive version of this figure is available over at ZEISS Online Tutorials ).
Surprisingly, the magnification of the objective lens does not affect the PSF—only the NA and wavelength matter.
You can use beads to measure PSFs for the objective lenses on your microscope to determine the resolution of each lens and also to see what condition each lens is in: the PSF of a damaged objective lens is often large and possibly skewed in one direction or another.
Figure 1: Interactive tutorial—The resolving power of an objective determines the size of the Airy diffraction pattern formed, and the radius of the central disk is determined by the combined NAs of the objective and condenser. Left image: image produced by smaller NA. Right image: increased resolution of image by increasing NA. You can access the interactive version of this tutorial over at ZEISS Online Campus.
Sometimes, a real specimen does indeed have single point-like fluorescent objects nicely separated from each other.
For example, cancer researchers studying the complicated process of DNA repair often irradiate cells and look to see what proteins localize on punctate sites of double-strand breaks.
These nuclear foci are small enough that you are actually observing the microscope’s PSF when you image them.
In many cases, however, your specimen is a complicated arrangement of closely spaced fluorophores, and the PSF is not apparent in your images.
Nevertheless, the PSF is hard at work, blurring out every fluorescent structure in your specimen as if tracing out the fine details with a fat paintbrush.
Figure 2: BSC-1 African Green Monkey Kidney Cells, 63x, stained with DAPI, Alexa 488 (Tubulin), Alexa 568 (TOMM20). ZEISS Axio Imager.Z2, Axiocam 506 mono, ApoTome.2 . Deconvolved image (ZEN software) on the right. Sample courtesy of Michael W. Davidson, The Florida State University.
Now, if we take the trouble to measure the PSF for a particular objective lens on our microscope, could we use what we know about the shape and size of the PSF to somehow undo its blurring influence in our specimen?
The answer is, “Yes!”. Mathematically, the blurring of the PSF with the actual arrangement of fluorophores in the specimen is called a convolution of the specimen with the PSF:
It’s no accident that the symbol for convolution ( ∗ \ast ∗ ) looks like a multiplication since the two operators are related.
We don’t know what the actual specimen looks like, but we record its image in the microscope, and we can also record the PSF.
An operation called deconvolution reverses the effect of the PSF on the specimen, much like the division operator reverses the effect of multiplication.
Practically speaking, we can never fully know what the specimen looks like, but by using iterative deconvolution algorithms we can remove some of the PSF’s blurring influence, particularly in the depth direction where the blur is worst.
Figure 2 shows the results of deconvolution.
Hopefully, this article has provided you with a good grasp of what the Point Spread Function is, how it affects your image, and what you can do to minimize these effects.
If you’re interested in delving deeper, head over to ZEISS Online Campus where you can find a chapter on The Point Spread Function , which goes into more detail about the maths underlying the PSF.
Originally published November 26, 2014. Reviewed and republished May 2021.
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The point spread is a margin of victory and you as a bettor determine which side will beat the margin. Learn more about what it means to cover the spread.
There are many ways to bet on sports but one of the most popular ways for football and basketball is called the point spread. The point spread is a margin of victory and as a bettor, you determine which side will beat the margin.
If this all sounds a bit foreign to you, this will be point spreads explained . We’re going to elaborate on exactly what the point spread means, go over the lingo and give you concrete examples of spread betting, so that you have a full understanding of point spreads after reading this article.
A spread is merely the margin of victory or a handicap in a given game. When you bet on the moneyline , you simply predict the outright winner of the game. When you bet the point spread, you’re betting on a margin set by the oddsmaker and you have to decide which side will “cover” or beat the spread.
The easiest way to explain this is with an example. We’ll use one of common NFL point spreads to take a closer look:
For point spread betting purposes, the first thing you’ll want to do here is notice either the ‘+’ or ‘-‘ sign as that will give you an important indication.
The plus sign indicates that this team will be receiving points. In this case, the Patriots will receive 2.5 points. The minus sign indicates that points will be losing points. In this case, the Cowboys will be losing 2.5 points.
What this means is that if you bet the Patriots, they are able to lose the game by two, one, tie or win the game, and you’d win your bet. As for the Cowboys, they’d have to win the game by three or more for you to cover.
A very basic way to do the math is to take the final score and add and subtract the points. For example, if the final score is. If you bet Dallas -2.5, then their final score of 30 – 2.5 = 27.5, which still beats out New England’s tally of 27 points. If the final score was Dallas 12, New England 10, you can see that New England +2.5 would put them at 12.5 points, which beats Dallas’ 12. That’s how does point spread work.
Now that you know how the spread works for each side, to play the point spread, all you have to do is determine which side you want to bet on. If you bet on Dallas -2.5, that’s one way to play the spread on that game. The other way would be to bet on New England +2.5.
If you’re calling in a bet over the phone or speaking to a cashier at a casino (in Vegas, etc.) then you’d merely say “I would like to bet on Dallas on the spread” or “I’d like to bet Dallas -2.5”. That’s how you play the point spread.
If you’re wondering how to read a point spread with the numbers after the spread itself, we’ll explain. Keep in mind that there are betting odds associated with each point spread. We’re going to show you what those mean and how to calculate them. Going back to our previous example, at a sportsbook like Bovada or BetOnline almost all point spreads will look like this:
As you can see, what’s been added here is the odds at the end of it. With -110 odds, that means for every $110 you bet on New England or Dallas, you’d win back $100 if they covered the spread.
The ‘-‘ sign denotes how much you have to bet to win $100. If there was a ‘+’ sign, that would denote how much you’d win if you bet $100. In other words, +150 means that if you bet $100, you’d win $150.
Keep an eye on how much sportsbooks charge for point spreads. Some books like Heritage Sports have low juice, so you can bet -105 on the spreads, which means you’ll save yourself a lot of money in the long run. The standard is -110, though.
The oddsmakers take a number of factors into account when it comes to setting a point spread. Those factors would include:
From a sportsbook’s perspective, the goal of a point spread is to split the action on both sides. The oddsmakers want to come up with a number where they can get equal bettors thinking the two sides can win, so that they can just get their “juice” (commission). Here’s what that looks like:
$1,100,000 of bets on the New England Patriots at +2.5 -110 $1,100,000 of bets on the Dallas Cowboys at -2.5 -110
What this means is that whoever ends up covering the spread, the betting sites pay out $1,000,000 in losses but collect $1,100,000. That $100,000 difference is what they’re going for every time.
The most popular way to bet on football and basketball is with the point spread and betting on the moneyline (the outright winner without worrying about points) is typically secondary. They’re known as spread betting sports. However, in the NHL and MLB, betting the moneyline is the primary way to bet on the games but there is still a point spread.
With hockey, you’ll see what’s called a puckline, which is a -1.5 and +1.5 line. Baseball will see something similar as they have a run line, which is -1.5 and +1.5.
Tennis is another sports where the main way to bet on the matches is the moneyline. However, if you bet on the point spread, it can be a spread on sets (I.E. a player has to win by 1.5 more sets than the other) or more commonly, a spread on games. So if a player is -7.5 games, they would have to win something like 6-2, 6-4, 6-2 to cover the spread.
If you’re wondering how the point spread works in boxing, we’ll explain. While most people tend to bet on the moneyline in boxing, you will occasionally see a spread on rounds won – especially for big championship bouts. This will be based on the official judges’ scorecards.
That means to beat the spread. The team that wins on the spread is the team that “covered”.
A forecasted number projected by the oddsmakers for which a stronger team (favorite) is supposed to defeat the weaker team (underdog).
The team that’s expected to cover the spread.
The team that’s not expected to cover the spread.
Betting on a team on the point spread on either side.
This allows you to move the point spread around a little bit by a 0.5 point, one point and sometimes more.
A push is when you tie on the point spread. You’ll get your money back. While some point spreads are on a half-number, many are on a whole number. So if the spread is -3 and a team wins by exactly 3 points, that’s considered a push.
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