Ok, let's go to the Maths then : the OTF gives you how spatial frequencies are transferred through your optical system. You understand that it is equivalent to an auto-correlation of the aperture, right? Well, if the aperture is circular (a disc function, for a perfect system), the auto-correlation is equal to the area of the intersection between two shifted discs (of equal radius). This shift represents the spatial frequency : at 0 spatial frequency (the DC component), the discs are aligning perfectly and you get the highest transfer (=1); at high frequency, the two circle are shifted a lot and you have only the area corresponding to a very small cat's eye shape; at the cut-off, only a single point is common between the two discs; finally, after the cut-off the two discs are not intersecting anymore and thus the transfer function is EQUAL TO 0.
In the case of your experiment, what was the cut-off frequency? (1.0/(Lambda F) where F is the F-Number of your optical system) Did you made measurements after that frequency?
Look closely at the first graph of the MTF in my previous link (in the EN page, top of the page). It represents your G function for a perfect system (no aberration, only the diffraction introduced by the finite size of the aperture). What you can see is that after the 1.0/(Lambda F) cut-off (500mm^-1 in that particular graph), everything will be equal to 0, thus the optical system is not transmitting any spatial frequencies larger than 500mm^-1.
This is not just "a couple of points", this is a hard physical limit to the resolution of your system.
True... up to the optical cut-off... After that NO optical system will transmit spatial frequencies... I was talking of this optical cut-off, you are talking of how to improve the system MTF before this cut-off...
No, there is a limit to resolution as your PSF (Point Spread Function, the image of a quasi-perfect point), is not a point but a pattern with finite size. Which means that the OTF/MTF couple has a limited support and your system CANNOT deliver any spatial frequencies beyond certain point (1.0/(Lambda F), where F is the F-Number of your system).
There is just one link to put in TFA : http://www.nature.com/nnano/journal/vaop/ncurrent/full/nnano.2014.31.html. Note that this paper never mentioned the word "contact lenses". So why? Why do we have instead a link to some stupid news site where they clearly don't have any clue on what they are talking about?
In your opinion, is it better than having Oculus VR bought by Microsoft?
"I felt a great disturbance in the Force, as if millions of nerd voices suddenly cried out in terror and were suddenly silenced. I fear something terrible has happened."
Actually no. This application is not working for broad wavelength spectrum and waste an awful lot of light in all the scenarios where you don't control the source (and impose it to be a laser).
OK, let's see : I am not familiar with this game and I don't know if you your selection and random event are ordered (not in the sense of the discussion on the sets we have but on the order of the events to appear : if I say, for example, 'HTH' does the sequence of random events must exactly match 'HTH' or 'HHT' and 'THH' are also considered a match)?
For the following few lines I will consider that this is true (while I think that it is false from the table you gave, but I don't think that it is changing anything on the model of the game we are debating on, correct me if I am wrong) :
Lets try to re-write in terms of clean Mathematics (boring but needed) : let P the set of possible events, P = {HHH, HHT,..., TTT}. The first player 'A' take an element called C_A form this set and, then, the second player chooses a element C_B from the set P\C_A (P set from which we remove C_A). Simple statistics (for balanced coins) give us that the probability of player A to win the game is 1/card(P) = 1/8, while the player 'B' has 1/card(P\C_A) = 1/7. We have then Pr('A wins on choice of C_A \in P') if(C_A==C_B) then return 1/card(P) otherwise return 1/(card(P)-1). This does not order the set as all weight are equals but not all the elements are equal (thus the set is not ordered by this relation). For example, we have f_HHH(HHT)=f_HHH(HTT) but not HHT==HTT.
Now I will try to conclude on the approach of the Food model (and the set named Foods) : the fitness function f_Contex(food) carries a Context variable that changes the score of each food. The Context can be adapted to the Nature and changes the favor the animals give to some source so if f_Context1(food_A) > f_Context1(food_B) > f_Context2(food_C) then it is more likely that for a large number of animal, they will choose food_A (mean). but this can change upon context change and have a reordering to f_Context2(food_B) > f_Context2(food_C) > f_Context2(food_A) without breaking transitivity in real world. It is just about finding a general enough model for the fitness/cost function (which is, I agree, very complex and probably impossible to reach). Then you have to rely upon some sort of piece-wise fitness functions, or I should say context-wise fitness function.
Maybe you need to refresh the definition of a comparison operator : Partially Ordered set. In short : you can not have an ordering comparison relation and not having transitivity for it. Period. So either it is an ordered set (like \mathbb{R}) and you can use a comparison operator or it is not (like \mathbb{C}) and you cannot use any ordering relation.
My point is more about the Mathematical objects rather than the thinking. Your last example does not matter as it is not an ordered set. Although, as I said in my first message, I think that they should not say that transitivity is broken but rather that the food attractiveness function can be changed by some events, thus reordering the elements in the set Foods. Or that Foods is not an ordered set and thus, no comparison operator can be applied.
Yes, but this has nothing to do with a violation of transitivity... It is just that their model for food attractiveness which was wrong. If you correct the model, then you should get back transitivity (basic optimizations rule).
Another big laugh at 1:30:45 : so they want a SMS messaging standardized library but they don't want to make a "niche" library for linear algebra in the standard? WTF???
Ok, for beam, you can choose between typical Gaussian structures such as Legendre-Gauss (Cartesian basis) or Laguerre-Gauss (cylindrical basis). In fact the current article is just about creating symmetric high order Laguerre-Gauss modes with a binary coded phase mask. These polynomials basis are modes of the propagation operator but not solution of Maxwell Eqs.
Any light structured wave (and not wavefront, that would be a 2D surface) can be decomposed on these basis but the waves which can be decomposed on a single of these mode will be conserved through propagation (if you have a mix, each of the mode will keep its structure but will have phase change against the other modes). And significantly blocking/altering one part of the beam WILL break propagation by changing the projection of the remaining beam over the basis.
Ok, so what about smooth wavefront modulation masks such as the Cubic Phase Mask or its Zernike-based counter-part which are doing exactly the same thing. They are not creating multiple focus but rather a single longitudinally elongated focus point (which is slightly larger than the Airy disk), they are not producing beams?
On your argument that this is not a beam : you cannot use the notion of photon, nor rays, because this is pure diffraction optics... Also, if you block the beam it will change the beam structure after propagation, because you won't have a mode of the diffraction operator anymore. The effect introduced is dependent on the size of the mask and its geometrical properties with respect to the incoming beam.
Slashdot Mirror
Ok, let's go to the Maths then : the OTF gives you how spatial frequencies are transferred through your optical system. You understand that it is equivalent to an auto-correlation of the aperture, right?
Well, if the aperture is circular (a disc function, for a perfect system), the auto-correlation is equal to the area of the intersection between two shifted discs (of equal radius). This shift represents the spatial frequency : at 0 spatial frequency (the DC component), the discs are aligning perfectly and you get the highest transfer (=1); at high frequency, the two circle are shifted a lot and you have only the area corresponding to a very small cat's eye shape; at the cut-off, only a single point is common between the two discs; finally, after the cut-off the two discs are not intersecting anymore and thus the transfer function is EQUAL TO 0.
In the case of your experiment, what was the cut-off frequency? (1.0/(Lambda F) where F is the F-Number of your optical system)
Did you made measurements after that frequency?
You can also read that kind of resource.
Look closely at the first graph of the MTF in my previous link (in the EN page, top of the page). It represents your G function for a perfect system (no aberration, only the diffraction introduced by the finite size of the aperture). What you can see is that after the 1.0/(Lambda F) cut-off (500mm^-1 in that particular graph), everything will be equal to 0, thus the optical system is not transmitting any spatial frequencies larger than 500mm^-1.
This is not just "a couple of points", this is a hard physical limit to the resolution of your system.
Oh, and what happens if G is equal to 0 after some spatial frequency (magnitude)?
True... up to the optical cut-off... After that NO optical system will transmit spatial frequencies...
I was talking of this optical cut-off, you are talking of how to improve the system MTF before this cut-off...
No, there is a limit to resolution as your PSF (Point Spread Function, the image of a quasi-perfect point), is not a point but a pattern with finite size. Which means that the OTF/MTF couple has a limited support and your system CANNOT deliver any spatial frequencies beyond certain point (1.0/(Lambda F), where F is the F-Number of your system).
Ha! I can just bend a piece of paper in matter of seconds... /sarcasm
This guys are jokes!
There is just one link to put in TFA : http://www.nature.com/nnano/journal/vaop/ncurrent/full/nnano.2014.31.html. Note that this paper never mentioned the word "contact lenses".
So why? Why do we have instead a link to some stupid news site where they clearly don't have any clue on what they are talking about?
Have you ever seen AdSense ads on Facebook?
No?
Now, you can!
We will buy your company for rand() * 1e11$!
In your opinion, is it better than having Oculus VR bought by Microsoft?
"I felt a great disturbance in the Force, as if millions of nerd voices suddenly cried out in terror and were suddenly silenced. I fear something terrible has happened."
Pew-pew-pew!
Should we understand that some of the articles posted on Slashdot are jokes then?
Actually no. This application is not working for broad wavelength spectrum and waste an awful lot of light in all the scenarios where you don't control the source (and impose it to be a laser).
If this was really working we wouldn't have had this wonderful article yesterday : http://science.slashdot.org/story/14/01/15/2349233/revolutionary-scuba-mask-creates-breathable-oxygen-underwater-on-its-own
& others probably (remember that article about Ctrl+Z for the ENTIRE internet?)...
OK, let's see : I am not familiar with this game and I don't know if you your selection and random event are ordered (not in the sense of the discussion on the sets we have but on the order of the events to appear : if I say, for example, 'HTH' does the sequence of random events must exactly match 'HTH' or 'HHT' and 'THH' are also considered a match)?
For the following few lines I will consider that this is true (while I think that it is false from the table you gave, but I don't think that it is changing anything on the model of the game we are debating on, correct me if I am wrong) :
Lets try to re-write in terms of clean Mathematics (boring but needed) : let P the set of possible events, P = {HHH, HHT, ..., TTT}. The first player 'A' take an element called C_A form this set and, then, the second player chooses a element C_B from the set P\C_A (P set from which we remove C_A). Simple statistics (for balanced coins) give us that the probability of player A to win the game is 1/card(P) = 1/8, while the player 'B' has 1/card(P\C_A) = 1/7. We have then Pr('A wins on choice of C_A \in P') if(C_A==C_B) then return 1/card(P) otherwise return 1/(card(P)-1). This does not order the set as all weight are equals but not all the elements are equal (thus the set is not ordered by this relation). For example, we have f_HHH(HHT)=f_HHH(HTT) but not HHT==HTT.
Now I will try to conclude on the approach of the Food model (and the set named Foods) : the fitness function f_Contex(food) carries a Context variable that changes the score of each food. The Context can be adapted to the Nature and changes the favor the animals give to some source so if f_Context1(food_A) > f_Context1(food_B) > f_Context2(food_C) then it is more likely that for a large number of animal, they will choose food_A (mean). but this can change upon context change and have a reordering to f_Context2(food_B) > f_Context2(food_C) > f_Context2(food_A) without breaking transitivity in real world. It is just about finding a general enough model for the fitness/cost function (which is, I agree, very complex and probably impossible to reach). Then you have to rely upon some sort of piece-wise fitness functions, or I should say context-wise fitness function.
hum, my bad : the following link is missing : http://en.wikipedia.org/wiki/Order_theory#Partially_ordered_sets
Maybe you need to refresh the definition of a comparison operator : Partially Ordered set. In short : you can not have an ordering comparison relation and not having transitivity for it. Period. So either it is an ordered set (like \mathbb{R}) and you can use a comparison operator or it is not (like \mathbb{C}) and you cannot use any ordering relation.
My point is more about the Mathematical objects rather than the thinking. Your last example does not matter as it is not an ordered set. Although, as I said in my first message, I think that they should not say that transitivity is broken but rather that the food attractiveness function can be changed by some events, thus reordering the elements in the set Foods. Or that Foods is not an ordered set and thus, no comparison operator can be applied.
Yes, but this has nothing to do with a violation of transitivity... It is just that their model for food attractiveness which was wrong. If you correct the model, then you should get back transitivity (basic optimizations rule).
Another big laugh at 1:30:45 : so they want a SMS messaging standardized library but they don't want to make a "niche" library for linear algebra in the standard?
WTF???
Ok, for beam, you can choose between typical Gaussian structures such as Legendre-Gauss (Cartesian basis) or Laguerre-Gauss (cylindrical basis). In fact the current article is just about creating symmetric high order Laguerre-Gauss modes with a binary coded phase mask. These polynomials basis are modes of the propagation operator but not solution of Maxwell Eqs.
Any light structured wave (and not wavefront, that would be a 2D surface) can be decomposed on these basis but the waves which can be decomposed on a single of these mode will be conserved through propagation (if you have a mix, each of the mode will keep its structure but will have phase change against the other modes). And significantly blocking/altering one part of the beam WILL break propagation by changing the projection of the remaining beam over the basis.
Ok, so what about smooth wavefront modulation masks such as the Cubic Phase Mask or its Zernike-based counter-part which are doing exactly the same thing. They are not creating multiple focus but rather a single longitudinally elongated focus point (which is slightly larger than the Airy disk), they are not producing beams?
On your argument that this is not a beam : you cannot use the notion of photon, nor rays, because this is pure diffraction optics... Also, if you block the beam it will change the beam structure after propagation, because you won't have a mode of the diffraction operator anymore. The effect introduced is dependent on the size of the mask and its geometrical properties with respect to the incoming beam.
"forming a pseudo non-diffrating "beam" --- which is a totally wrong way to describe this."
Hum... Why?
Yeah, except when the object IS the source...
And because all objects are sources... (except when at a temperature of 0 Kelvin and black holes)
Which is ok for point source but not for large objects.
YAMT : Yet Another Misleading Title...