Wu, Q., Ren, Z.: Study of the nonparaxial propagation of asymmetric Bessel–Gauss beams by using virtual source method. Opt. Commun. 432, 8–12 (2019). https://doi.org/10.1016/j.optcom.2018.09.039

Stoian, R., Bhuyan, M.K., Zhang, G., et al.: Ultrafast Bessel beams: advanced tools for laser materials processing. Adv. Opt. Technol. 7(3), 165–174 (2018). https://doi.org/10.1515/aot-2018-0009

Flat lighting is a common occurrence in photography, as flat lights can either be accidental or deliberate. You get flat lights mostly when you put broad and ...

We were recommending against variable density ND filters in our stores all the way back into the mid 2000's. Yes, we still sold them, but the customer left the stores knowing what to watch for when using them. Some higher end VNDs have added physical stops that prevent over-rotation which helps reduce if not eliminate the cross filtration issue. But the "not dark enough" problem remains for many applications.

For long exposure photography, it’s not about the filter you’re using but about the exposure you need for the desired effect. You can’t simply buy a 10-stop neutral density filter and be done with it. There will be situations where that filter isn’t strong enough. In other situations, the filter is much too strong.

Durnin, J., Miceli, J.J., Eberly, J.H.: Diffraction-free beams. Phys. Rev. Lett. 58, 1499–1501 (1987). https://doi.org/10.1103/PhysRevLett.58.1499

Well... Canon EF-EOS R adapter with variable nd filter slot doesn't have any crosshair effect, yet it sits between the lens and body. 1-7 stop is covering quite a lot because when combined with 3 or 4 stop GND in most situations when shooting sunrise or sunset that's all you need. And it works with all our 14 lenses! Attached photo was shot on Laowa 12/2.8 zero D on FF camera.

Whittaker, E.T.: On the partial differential equations of mathematical physics. Math. Ann. 57(3), 333–355 (1903). https://doi.org/10.1007/BF01444290

Bagini, V., Frezza, F., Santarsiero, M., et al.: Generalized Bessel–Gauss beams. J. Mod. Opt. 43(6), 1155–1166 (1996). https://doi.org/10.1080/09500349608232794

The crosshair effect that can be seen in photography is less of a problem for video. In most cases, a 16:9 or 16:10 aspect ratio is used. Since the darkening of the frame due to the crosshair effect starts in the corners of the frame, it won’t show up unless the neutral density is turned to the extremes.

Besselbeam

It’s not only the desired exposure that dictates which neutral density filter is necessary. The weather situation and time of day also influence. That’s why it’s important to have a selection of neutral density filters at hand.

If you’re familiar with video, you know how important shutter speed or shutter angle is. If you also want to have control of the depth of field, there is only one way to get the proper exposure: the ISO value. But the ISO value also has limitations if you’re shooting in the log format.

El Halba, E., Boustimi, M., Ez-zariy, L., et al.: Propagation characteristics of Bessel-like beams through ABCD optical system. Opt. Quant. Electron. 49(8), 1–11 (2017). https://doi.org/10.1007/s11082-017-1099-z

The best way is to invest in a set of real neutral density filters. Start with a 3-stop and a 10-stop. Depending on your needs, you can expand to a 6-stop or even a 15-stop.

Kotlyar, V.V., Kovalev, A.A., Soifer, V.A.: Asymmetric Bessel modes. Opt. Lett. 39(8), 2395–2398 (2014b). https://doi.org/10.1364/OL.39.002395

Thank you for adding the focal length. I forgot to mentioned it (didn't think if it, to be honest :)) Magnetic ND filters is a perfect alternative for the large square filters.

This is the variable neutral density filter. A filter that allows you to change the neutral density just by dialing in the amount. There are a lot of different variants available. Some allow a neutral density that ranges up to 10 stops or even more.

Liu, H., Hu, Z., Xia, J., et al.: Generation and applications of non-diffraction beam. Acta Phys Sinica (Ch Ed) 67(214), 204 (2018). https://doi.org/10.7498/aps.67.20181227

Planchon, T.A., Gao, L., Milkie, D.E., et al.: Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination. Nat. Methods 8(5), 417–423 (2011). https://doi.org/10.1038/nmeth.1586

Gutiérrez-Vega, J.C., Iturbe-Castillo, M.D., Chávez-Cerda, S.: Alternative formulation for invariant optical fields: Mathieu beams. Opt. Lett. 25(20), 1493–1495 (2000). https://doi.org/10.1364/OL.25.001493

Chafiq, A., Hricha, Z., Belafhal, A.: Paraxial propagation of Mathieu beams through an apertured ABCD optical system. Opt. Commun. 253(4), 223–230 (2005). https://doi.org/10.1016/j.optcom.2005.04.068

Yes, indeed. Cropping will definately influence the visibility in stills. But there is a tendency to keep the aspect ratio of the camera sensor while cropping, although there is no need for it.

"A variable ND filter is intended for videography. It offers a way of controlling the exposure. Due to the aspect ratio (16:9 and 16:10), any crosshair effect will be outside the frame."

Pei, S., Xu, S., Cui, F., et al.: Propagation of a Bessel–Gaussian beam in a gradient-index medium. Appl. Opt. 58(4), 920–926 (2019). https://doi.org/10.1364/AO.58.000920

Gaussianbeamq parameter

Kotlyar, V.V., Stafeev, S.S., Porfirev, A.P.: Tight focusing of an asymmetric Bessel beam. Opt. Commun. 357, 45–51 (2015). https://doi.org/10.1016/j.optcom.2015.08.084

COMSOL Gaussianbeam

This effect slowly creeps into the frame. It will be easily visible in a bright sky or flat surfaces, but if there is a lot of contrast, it will go unnoticed while photographing. But it will be visible during post-processing. In the worst-case scenario, a variable neutral density filter will make the photo unusable.

ProMaster makes some VND filters that address these problems very well. They have an X mark on the filter ring that easily identifies where the crosshair effect will begin with a wide lens. By doing that they don't have to severely limit their range like companies such as Polar Pro do. They also have an Extreme VND with a range of 5 to 12 stops. I'm a still photographer only, and I always carry single density NDs unless I'm backpacking or traveling light. During those times I carry two ProMaster VNDs, their standard range and the extreme range. They work amazingly well, especially when every ounce counts.

This amount of filters can be expensive, especially if you choose good quality. To prevent the need for filters for every lens diameter you have, a filter holder and square filters are preferable. I use the Haida Red Diamond 100mm filters with excellent results, even if two filters are combined. But this is not about the brand; it’s about the costs and the need for a relatively large filter holder and filters. You also need extra space inside the bag to carry this around.

Kovalev, A.A., Kotlyar, V.V.: Lommel modes. Opt. Commun. 338, 117–122 (2015). https://doi.org/10.1016/j.optcom.2014.09.082

Tricomi beams are structured light beams that belong to the general class of non-diffracting light beams. The cross-section of an ideal Tricomi beam extends upto infinity and hence the energy distribution in the transverse plane (beam cross-section) is not finitely bounded. But all real-world systems are finitely bound, which causes inconvenience in studying Tricomi beams practically. To overcome this issue we introduce Tricomi–Gauss beam for the first time, which possesses similar characteristics to Tricomi beams but with a finite beam cross-section. In this study, we derive the general expression for the Tricomi–Gauss beam and its propagation. We show that the derived equation can be used to study the propagation properties of a family of Bessel–Gauss beams only by setting the appropriate parameters to the derived equation. Simulation results show the intensity and phase profiles of the beams as they propagate through (i) free space (ii) lens system and (iii) fractional Fourier transform system. Interesting propagation characteristics were observed, especially in the case of the asymmetric Bessel–Gauss beam, which can be attributed to the choice of parameters. The advantages of Tricomi–Gauss beam are verified by practically generating the beams using computer-generated holography technique.

Jackin, B., Palanisamy, P.: A completely open source based computing system for computer generation of Fourier holograms. Comput. Phys. Commun. 180(10), 1882–1887 (2009). https://doi.org/10.1016/j.cpc.2009.04.014

Capturing landscapes with long exposures is popular. It can lead to great results when performed correctly. The right exposure time depends on the situation and the desired result.

Belafhal, A., Ez-Zariy, L., Hennani, S., et al.: Theoretical introduction and generation method of a novel nondiffracting waves: Olver beams. Opt. Photonics J. 5(07), 234 (2015). https://doi.org/10.4236/opj.2015.57023

Gaussianbeampropagation simulation

I recently purchased an Urth vario neutral density filter, but I'm extremely disappointed with its performance. The cross hair effect makes it completely unusable, and I'm unable to fit my lens hood back on with the filter attached. When I requested a refund from Urth, they simply blamed me and suggested that I use the filter on a different lens with the same filter size. Additionally, they mentioned that it can't be used on wide angle or telephoto lenses, so does that mean it's only compatible with 50mm lenses?

Guizar-Sicairos, M., Gutiérrez-Vega, J.C.: Generalized Helmholtz–Gauss beam and its transformation by paraxial optical systems. Opt. Lett. 31(19), 2912–2914 (2006). https://doi.org/10.1364/OL.31.002912

If long exposures are preferred, there are limits to how far you can go unless you wait for darkness. The best alternative is a neutral density filter, which allows the desired long exposure at any time of day. Whatever you do, don’t use a variable neutral density filter for photography.

It has and alway will have effect because light at especially wide angle lenses will come from an angle when hitting the filter ... VND is like polariser ( have you ever turn polariser too far on wide angle lens to see one side of photo darker than the other side?) and therefor having filter between lens and body where light is going straight and not in and angle will affect multiple properties such as crosshair, contrast, flare, etc...

Bayraktar, M., Başdemir, H.D.: Cylindrical-sinc beam. Optik 125(19), 5869–5871 (2014). https://doi.org/10.1016/j.ijleo.2014.07.054

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Although no rule prohibits you from using a variable neutral density filter for photography, I advise being cautious. Always keep an eye out for the darkened crosshair effect. It’s difficult to spot in the viewfinder or on the LCD screen, but it will be noticeable in the end.

A lot of filters are limited to 6-stop or 7-stop. Some offer a 10-stop, which extends a normal exposure 1,000 times. But there is a bigger issue with these filters.

高斯光束

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Kotlyar, V.V., Kovalev, A.A., Skidanov, R.V., et al.: Asymmetric Bessel Gauss beams. J. Opt. Soc. Am. A 31(9), 1977–1983 (2014a). https://doi.org/10.1364/JOSAA.31.001977

However, if the strength of the water has to be visible, often an exposure between a fourth of a second and two seconds is preferable. For mountain streams and waterfalls, the exposure has to be different as well. Again, it depends on the speed of the water, the focal length, and the desired effect.

I use the Haida NanoPro CPL-VND filter with a neutral density range of 3 stops up to 7 stops. It’s perfect for most situations. The benefit of this filter is the built-in polarization effect as well. Although the beginning of a darkening crosshair effect is visible in photography when dialed to 7 stops, it’s nearly imperceptible for video.

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The variable neutral density filters use two polarization filters to increase the density of the filter. By rotating a polarization filter in front of another, less and less light will be allowed to pass through the filters.

Select index from list of Edmund Optics' own optical substrates to help calculate focal lengths and principal points of any standard lens.

Sokolovskii, G.S., Dudelev, V.V., Losev, S.N., et al.: Optical trapping with Bessel beams generated from semiconductor lasers. J. Phys: Conf. Ser. 572(1), 012039 (2014). https://doi.org/10.1088/1742-6596/572/1/012039

laguerre-gaussian modes

Havelock, T.: Mathematical analysis of wave propagation in isotropic of p dimensions. Proc. Lond. Math. Soc. 2(1), 122–137 (1905)

Oct 23, 2024 — Furthermore, pancake lenses has better image clarity and sharpness than fresnel lenses. Meta Quest 3S: It has Fresnel lens with 3 position IAD ...

I just started using variable ND Filter, I didn't notice yet any problem, but maybe I wasn't aware so I missed it. My filter can make a total darkness. Thanks for the tip I will carefully be looking for the phenomena.

The position of the filter should not have an effect on the appearance of the cross hair effect. I'm happy to hear it doesn't appear.

Wouldn’t it be wonderful if you could buy just one filter and be done with it? It saves a lot of money, and it’s much easier to carry around with you. Just buy one large filter, like 82mm or 86mm. Use step-up rings to fit the filter onto lenses with a smaller diameter.

Eyyuboğlu, H.T., Bayraktar, M.: Propagation properties of cylindrical sinc Gaussian beam. J. Mod. Opt. 63(17), 1706–1712 (2016). https://doi.org/10.1080/09500340.2016.1170902

The authors have no competing interests as defined by Springer, or other interests that might be perceived to influence the results and/or discussion reported in this paper.

The cross hair effect is for incompetent variable ND filter users. Competent users know how to use the variable ND without the cross hair issue. Yes, it isn't as dark as some, but for a lot of situations it works like a charm and saves buying all the densities it covers including the infinite amount between. Need more? Get a more powerful one as well.

S.K.S and B.J.J conceived the idea, S.K.S did the simulations and experiments, K.K, N.T and W.S helped with the experiments and provided suggestions, S.K.S wrote the main manuscript B.J.J supervised the research. All authors reviewed the manuscript.

Sometimes an extremely long exposure is needed to remove every trace of movement from the water. It’s often used for fine art or something similar. Exposures of minutes are not uncommon.

The first problem you encounter is the limited range of neutral density. Although there are unbelievably large ranges available, most variable filters are not dark enough for really long exposures. If you want more than 30 seconds during daylight, you are lucky to achieve that exposure with a variable neutral density filter.

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Singh, S.K., Haginaka, H., Jackin, B.J., et al.: Generation of Ince–Gaussian beams using Azocarbazole polymer CGH. J. Imaging 8(5), 144 (2022). https://doi.org/10.3390/jimaging8050144

Durnin, J.: Exact solutions for nondiffracting beams. I. The scalar theory. J. Opt. Soc. Am. A 4(4), 651–654 (1987). https://doi.org/10.1364/JOSAA.4.000651

A lot of these filters produce terrible results, especially the cheaper ones. If a filter promises a huge range, you can be sure it doesn’t live up to its expectations. But even the expensive ones, with a limited neutral density range, are best to be avoided, at least for photography.

Mphuthi, N., Gailele, L., Litvin, I., et al.: Free-space optical communication link with shape-invariant orbital angular momentum Bessel beams. Appl. Opt. 58(16), 4258–4264 (2019). https://doi.org/10.1364/AO.58.004258

Siviloglou, G.A., Christodoulides, D.N.: Accelerating finite energy airy beams. Opt. Lett. 32(8), 979–981 (2007). https://doi.org/10.1364/OL.32.000979

Looking at the effects a variable neutral density filter can have, it seems these filters are unusable for photography. However, a variable neutral density filter is perfect for video.

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

McLaren, M., Agnew, M., Leach, J., et al.: Entangled Bessel–Gaussian beams. Opt. Express 20(21), 23589–23597 (2012). https://doi.org/10.1364/OE.20.023589

Arrizón, V., Ruiz, U., Carrada, R., et al.: Pixelated phase computer holograms for the accurate encoding of scalar complex fields. J. Opt. Soc. Am. A 24(11), 3500–3507 (2007). https://doi.org/10.1364/JOSAA.24.003500

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If long exposure photography is your thing, you are best off carrying three or even four neutral density filters with you. You need a 3-stop, a 6-stop, a 10-stop, and a 15-stop to be prepared for every situation and desired effect. It also allows you to combine multiple neutral density filters, extending the number of possible densities.

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VNDs use paired circular polarization filters to do their job, and I have seen images where half of the view has the polarization effect gradually tapering off to the other half with reduced polarization (clouds on a bright day). Again, just be aware of your tools and what their limitations are.

Garcés-Chávez, V., McGloin, D., Melville, H., et al.: Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam. Nature 419(6903), 145–147 (2002). https://doi.org/10.1038/nature01007

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The VND problem can be serious on wide angle lenses, so it does rule out their use for those sweeping views of lakes, mountains and deserts. Vloggers can also see the effect if they use wide lenses equivalent to 20mm and wider on full frame. I made the mistake of buying a pricey 82mm VND and passed it on to a video shooter. I much prefer circular magnetic filters for stills because I can change nd values in seconds and there’s no chance of light leakage on very long exposures. I have abandoned rectangular filters and the clumsy holders, which you need for graduated nds. This is because the gradient effect is always linear, unlike most of the high contrast subjects out there. I can usually do a better job in processing and can always take a couple of different exposures as insurance in extreme situations, for example with the sun over the sea, which is about the only situation where a square grad is nearly as good!

Forbes, A., de Oliveira, M., Dennis, M.R.: Structured light. Nat. Photonics 15(4), 253–262 (2021). https://doi.org/10.1038/s41566-021-00780-4

Collins, S.A.: Lens-system diffraction integral written in terms of matrix optics\(\ast \). J. Opt. Soc. Am. 60(9), 1168–1177 (1970). https://doi.org/10.1364/JOSA.60.001168

Could it be argued that if you choose 16:9 for images instead of video then the crosshair effect would be eliminated. Not saying I'd do this but just wondering.

Singh, S.K., Kinashi, K., Tsutsumi, N. et al. Tricomi–Gauss beam and its propagation characteristics. Opt Quant Electron 55, 352 (2023). https://doi.org/10.1007/s11082-023-04626-x

Indeed, if you're aware of the effect you can try to avoid it. But it comes at a cost of less dark filters. If you need to buy more VND filters of different strengths, you might as well buy three regular ND filters. This way you avoid the effect completely. Regarding the infinite amount of densities, it rarely needed - speaking from years of experience.

Engelbrecht, C.J., Stelzer, E.H.: Resolution enhancement in a light-sheet-based microscope (SPIM). Opt. Lett. 31(10), 1477–1479 (2006). https://doi.org/10.1364/OL.31.001477

Absolutely agree. I use mine solely for video work. The crosshair issue I only see when using very wide-angle lenses, and it depends on the brand.

Santarsiero, M.: Propagation of generalized Bessel–Gauss beams through ABCD optical systems. Opt. Commun. 132(1), 1–7 (1996). https://doi.org/10.1016/0030-4018(96)00298-2

Nando Harmsen is a Dutch photographer that is specialized in wedding and landscape photography. With his roots in the analog photo age he gained an extensive knowledge about photography techniques and equipment, and shares this through his personal blog and many workshops.

VND filters are marked so if used properly there will be NO dark cross etc. Only people who fail to use the filters as designed get the dark cross. They are wonderful, no they don’t get real dark but for most general use are awesome.

Cao, Z., Zhai, C., Xu, S., et al.: Propagation of on-axis and off-axis Bessel beams in a gradient-index medium. J. Opt. Soc. Am. A 35(2), 230–235 (2018). https://doi.org/10.1364/JOSAA.35.000230

Gaussianbeamcalculator

Lu, D.Q.: Generalized Tricomi and Hermite–Tricomi functions. Appl. Math. Comput. 218(9), 5090–5098 (2012). https://doi.org/10.1016/j.amc.2011.10.074

S.K.S. acknowledges the Ministry of Education, Sports, and Culture of Japan (MEXT) scholarship provided by the Japanese Government for his studies at the Kyoto Institute of Technology.

laguerre-gaussianbeam

Since the light that passes through a polarization filter is directional, two will form a darkened cross in the frame. The more you rotate the filters relative to each other, the stronger the effect will occur.

[headline]: YOU SHOULDN’T BE USING VND FILTERS [after jumping to recipe and scrolling past all the ads on the page]: …but also here are the reasons why it’s fine if you do

This results in limitations while filming under bright situations. That’s when a variable neutral density filter comes in. It offers a way of controlling the exposure without losing control of the shutter speed and depth of field.

Zhu, J., Zhu, K., Ding, N., et al.: Tricomi beams and nondiffracting sheet beams. Results Phys. 28(104), 627 (2021). https://doi.org/10.1016/j.rinp.2021.104627