3D Partial Dispersion Diagram
Explore glasses in 3D using one Abbe number and two partial dispersions as axes.
FAQ
Partial dispersion is used to describe the color dependence (also known as dispersion) of the refractive index over a narrower range of wavelengths.
It is typically calculated by taking the difference in the refractive index of a material at two different
wavelengths $n_x - n_y$ and dividing it by the difference in the refractive index of the material at the F and C wavelengths $n_F - n_c$.
$$P_{x, y} = \frac{n_x - n_y}{n_F - n_c}$$
At AbbeTrex, we replace the F and C wavelengths with the short, long, and x wavelengths, respectively, to get the following equation:
$$P_{y} = \frac{n_{short} - n_y}{n_{short} - n_{long}}$$
Our version of partial dispersion, is setup to help find glasses that are best for your design range, without having to think about specific wavelengths and to making the approach functional beyond the NIR range. We chose partial dispersions that match the abbe number stategy used in our achromat design tool. Those partial dispersions ranges will be 1/4 and 1/2 of the range. For example, if your design range is 0.5-1.0 μm, the partial dispersion will be calculated for 0.5-0.625 μm and 0.5-0.75 μm.
If you want to read more about dispersion, you can read this Wikipedia article.
$$P_{x, y} = \frac{n_x - n_y}{n_F - n_c}$$
At AbbeTrex, we replace the F and C wavelengths with the short, long, and x wavelengths, respectively, to get the following equation:
$$P_{y} = \frac{n_{short} - n_y}{n_{short} - n_{long}}$$
Our version of partial dispersion, is setup to help find glasses that are best for your design range, without having to think about specific wavelengths and to making the approach functional beyond the NIR range. We chose partial dispersions that match the abbe number stategy used in our achromat design tool. Those partial dispersions ranges will be 1/4 and 1/2 of the range. For example, if your design range is 0.5-1.0 μm, the partial dispersion will be calculated for 0.5-0.625 μm and 0.5-0.75 μm.
If you want to read more about dispersion, you can read this Wikipedia article.
The Abbe number describes how much the refractive index of a material changes with wavelength (dispersion): a lower Abbe number means colors travel over a wider range of speeds through the material.
It is computed from the index of refraction at your chosen short, center, and long wavelengths: $V = (n_{center}-1)/(n_{short} - n_{long})$, where $n_{short}$, $n_{center}$, and $n_{long}$ are the refractive indices at those wavelengths. So the X axis uses the same Abbe number as on the main Abbe diagram, but evaluated over the same wavelength range you set for the partial dispersion plots.
If you want to read more, see this Wikipedia article on the Abbe number.
It is computed from the index of refraction at your chosen short, center, and long wavelengths: $V = (n_{center}-1)/(n_{short} - n_{long})$, where $n_{short}$, $n_{center}$, and $n_{long}$ are the refractive indices at those wavelengths. So the X axis uses the same Abbe number as on the main Abbe diagram, but evaluated over the same wavelength range you set for the partial dispersion plots.
If you want to read more, see this Wikipedia article on the Abbe number.
The best fit line is found using the average of all the partial dispersion data with the Abbe number as a reference.
Then the distance of each point from the line can be calculated and used to create the deviation of partial dispersion plot.
Most of the resulting partial dispersion data ends up together on one about one plane, but when looking for 4 different glasses for chromatic design, they cannot be on the same plane. To show the deviation from a plane, The best fit plane is found using the singular value decomposition of the residuals of the partial dispersion data around the best fit line. This plane is then used to create the plane deviation of partial dispersion plot.
Most of the resulting partial dispersion data ends up together on one about one plane, but when looking for 4 different glasses for chromatic design, they cannot be on the same plane. To show the deviation from a plane, The best fit plane is found using the singular value decomposition of the residuals of the partial dispersion data around the best fit line. This plane is then used to create the plane deviation of partial dispersion plot.
This tab shows the distance of each glass point from the best-fit line.
The best-fit line is the average of all partial dispersion data with the Abbe number as reference.
The plot lets you see how much each material's partial dispersion deviates from that line, so that you can better select glasses for an apochromat.
This tab shows how each point deviates from the best-fit plane.
The best-fit plane is found using singular value decomposition of the residuals of the partial dispersion data around the best-fit line.
For chromatic design with four different glasses, usually for a super achromat, the glasses cannot all lie on the same plane.
This plot helps you pick a glass off the plane for the most strongly corrected achromats.
Choose the short, center, and long wavelengths to match the wavelength range of your optical design or application.
The partial dispersions are computed over your range and over sub-ranges at 1/4 and 1/2 of that range (as in the achromat design tool), so the range should reflect where you need to correct chromatic aberration.
For visible designs you can use the classic F-C style range (e.g. short ≈ 0.486 μm, center ≈ 0.588 μm, long ≈ 0.656 μm). For NIR or other bands, set the three wavelengths to span your band of interest; the tool works for any range, not only the visible.
For visible designs you can use the classic F-C style range (e.g. short ≈ 0.486 μm, center ≈ 0.588 μm, long ≈ 0.656 μm). For NIR or other bands, set the three wavelengths to span your band of interest; the tool works for any range, not only the visible.
In the 3D partial dispersion diagram, an apochromat uses three glasses, whose points form a triangle in partial-dispersion space.
Select three glasses so that this triangle has the largest possible area-i.e. the points are as spread out as possible in the plot.
That spread gives the best leverage for correcting chromatic aberration at three wavelengths.
The Deviation of Partial Dispersion tab can help you find glasses that sit far from the best-fit line and thus contribute to a larger triangle.
As a general rule of thumb, one of your glasses should be in the flourite/extra-low dispersion group. A common example from Schott is N-PK52A. A common classical example is calcium fluoride (CaF2). Read more about flourite glasses here: Wikipedia article on low-dispersion glasses.
As a general rule of thumb, one of your glasses should be in the flourite/extra-low dispersion group. A common example from Schott is N-PK52A. A common classical example is calcium fluoride (CaF2). Read more about flourite glasses here: Wikipedia article on low-dispersion glasses.
A super achromat uses four glasses; their points in the 3D partial dispersion diagram form a tetrahedron.
Select four glasses so that this tetrahedron has the largest possible volume-i.e. the four points are as spread out as possible in 3D and not all on one plane.
That maximizes the correction capacity at four wavelengths.
The Plane Deviation tab helps you find glasses that lie off the best-fit plane, which you need for the fourth vertex of a large-volume tetrahedron.
As a general rule of thumb, one of your glasses should be in the flourite/extra-low dispersion group. A common example from Schott is N-PK52A. A common classical example is calcium fluoride (CaF2). Read more about flourite glasses here: Wikipedia article on low-dispersion glasses.
As a general rule of thumb, one of your glasses should be in the flourite/extra-low dispersion group. A common example from Schott is N-PK52A. A common classical example is calcium fluoride (CaF2). Read more about flourite glasses here: Wikipedia article on low-dispersion glasses.
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