Numerical Aperture calculator

We have one of those but Ive never tested it, and haven’t found a specific usecase for it. If anybody in this thread has some nice examples for use of this lens, it would be appreciated if you could share.

Recall that NA = RI*sin(α), so NA < medium refractive index… unless you figure out how to collect light with more than 90° half-angle. The Olympus 1.7 NA uses a special coverslip and special immersion oil with RI > 1.7. The medium with refractive index called out in this equation is the medium the objective is designed for (i.e. the immersion medium for oil objectives).

I don’t think having a higher NA will degrade your imaging, but it is possible that on the manufacturer side, focusing on achieving higher NA will yield a tradeoff with something such as planeity and field of view size. This follows what @DanMetcalf mentioned.

What fabulous answers! As kind of mentioned in the other answers, sample prep and RI of mounting and sample are important, and the WD of super high NA objectives do limit to 100nm or less typically. One thing I know the reps (particularly my local Olympus reps, really honest), always remind me of, in addition to the importance of sample prep, is that to harness maximally achievable NA of any objective, you need to fill the back aperture adequately, e.g. just throwing a higher NA modern objective lens onto an older system won’t necessarily give you better performance if you’re starved for photons getting to the sample, I’ve experienced this myself by comparing my current Olympus 40X 1.30 oil to their new XApo 1.40 oil, on a middle aged Yokogawa spinning disk. Great discussion of this topic!

For resolution and image quality, I want to mention that at least Olympus confirmed that their 1.5 NA lens has much better image quality than 1.7NA in terms of aberration correction.

Well I believe that you are correct, and that the higher NA objectives don’t collect more light. According to this web-page (Leica) an objective has a typical maximum collection angle of about 144 degrees. Doing the math for an oil immersion objective gives an NA of 1.44 as the maximum assuming 1.515 for the refractive index. As you say, you will get additional collection if the dye is within a few hundred nanometers of the interface because it will preferentially emit into the higher index media (SAF), but I think you are asking about ‘deep’ in the sample?

There are also really high NA lenses, like 1.57 100x lenses*. (sorry I read over the olympys 1.7 NA lens mentioned in the first post) I think those can be used to do TIRF in fixed samples, but do require a different material coverslip and hi refractive index oil. I wonder if there are any publication of using these type of lens in SMLM and if there is any benefit of the increased resolution.

I would be interested in getting the response from an objective manufacturer. Here is my take, which is slightly different than @Hazen_Babcock.

I have asked this issue from Nikon and Olympus, they helped a lot, but I still need more clear answer and no one suggested a side by side test (although I believe that side by side comparison would not be very accurate). I think the problem is that I am talking about biological samples (which I am sure that most of us working with them). Any objective lens can only observe the lights that come out of the sample. The sample medium has RI about n1=1.38, so even an objective lens can gather all 180 degree of emission light (180 degree inside the sample) we can put at most 1.38 on the other side of Snell’s law to calculate the maximum angle of gathering light: 1.38 = n2sin(a)*. Please note that (a) gives us the maximum refraction angle of light from sample to cover slip and oil (except the evanescent field and SAF) which is about 65 degree for normal oil (1.52) and of course is equal to critical angle that we use in TIRF. see So it seems no matter what lens and what oil you are using, from a biological sample you cannot gather light from larger angle than critical angle. Yes higher NA can collect more light, but here there is no more incoming light to collect; if you are using other samples (n1) this would be different. However, these lenses are usually used for TIRF illumination or at least short WD imaging, so no one can neglect SAF. This is what I think at the moment; am I right?

To your question of whether having more NA will compromise image quality, I would say “no” but also be aware that objectives have been designed to perform different tasks and use caution when trying to repurpose them. For example, I am aware of several objectives designed for multi-photon imaging where the PSF size on a camera is significantly larger than the NA would predict. For multi-photon imaging this is acceptable, but if you use on a lightsheet system beware. So indeed it is possible for lenses to have intrinsic “underperforming” resolving power relative to the NA-based theoretical limit. I am not aware of any TIRF lenses with this problem. It is also possible for objectives to get damaged or poorly assembled in a way that they don’t achieve anywhere near the theoretical resolving performance.

Edmund Optics offers all TECHSPEC® lenses with an optional single-layer, dielectric anti-reflection (AR) coating to reduce surface reflections. In addition, custom single-layer, multi-layer, V, and 2V coatings are available for both our off-the-shelf and large volume custom orders. View Custom Optical Lens Coatings for information.

Broadband anti-reflection (BBAR) coatings are designed to improve transmission over a much wider waveband. They are commonly used with broad-spectrum light sources and lasers with multiple-harmonic generation. BBAR coatings typically do not achieve reflectivity values quite as low as V-coats but are more versatile because of their wider transmission band. In addition to being applied to transmissive optical components including lenses and windows, AR coatings are also used on laser crystals and nonlinear crystals to minimize reflections, as Fresnel reflections occur where air and the crystal meet.1

Numerical aperture unit

NIR I and NIR II: Our near-infrared I and near-infrared II broadband AR coatings offer exceptional performance in near-infrared wavelengths of common fiber optics, laser diode modules, and LED lights.

I have a very basic question about objective lenses with NA larger than ~1.4: can for instance a 1.49 NA lens gather more light than a 1.4 (1.33 to 1.38) NA lens from a biological sample? To me it seems that this larger area only participate in especial illumination method like TIRF, while no more light from a sample is possible to be observed through these zone, regardless of the NA of lens (except for SAF ring and very few hundreds of nm depth of sample). In general, I am not sure how they can gather more light and generate brighter or higher resolution images; can they? Can they have better resolving power based on their higher NA for example when they are used in trans-illumination, side-illumination (or prism-based TIRF) light-sheet illumination? Also, what is their critical role (if any) in super resolution microscopy such as PALM/STORM? My main concern is that these extra NA may compromise image quality and thus the resolution to some extent. (Olympus 1.7NA) I am sorry if my question looks very basic and stupid.

Telecom-NIR: Our telecom/near-infrared is a specialized broadband AR coating for popular telecommunications wavelengths from 1200 – 1600nm.

Numerical aperture of microscope

Because reflectivity increases rapidly as the wavelength of the source moves further away from the DWL, optical components with V-coats are meant for use at exactly or very close to the intended DWL of the coating. An interesting characteristic of V-coats is that the shape of their transmission curves is semi-periodic such that the reflectivity reaches a local minimum at harmonics of the DWL (e.g. $ \tfrac{\lambda_0}{2} $ or $ \tfrac{\lambda_0}{4} $) that are not as optimized for reflectivity as at the DWL. V-coats are usually comprised of only two coating layers. Simple V-coats can consist of a single layer with a thickness of a $ \tfrac{\lambda}{4} $, but more layers may be required to adjust the bandwidth or if a coating material with an appropriate index of refraction is not available. Multilayer coatings may also compensate for different angles of incidence, but are more complicated and tend to have larger bandwidths. If the thickness of the V-coat layers is incorrect, the reflectivity of the coating increases and the DWL changes. V-coats from Edmund Optics typically achieve minimum reflectivities significantly less than 0.25%, but all standard V-coats have specified reflectivities of <0.25% at the DWL. This allows for small shifts in the DWL from coating tolerances.

Objective lenses that have NA/RI ratio anywhere near the maximum of 1.0 (i.e. large collection angles) usually have very short working distance because otherwise they would have a huge front aperture. TIRF lenses fall into that category. I believe than a NA 1.49 TIRF (standard oil) objective really does have a arcsin(1.49/1.5128) ~= 80 degree collection angle, but it has a tiny working distance (BTW the working distance specified is the free working distance besides the coverslip, if one is specified). For TIRF you are imaging right at the coverslip surface anyway so you don’t need more than the 10s of micron WD anyway.

UV-AR and UV-VIS: Ultraviolet coatings are applied to our UV fused silica lenses and UV fused silica windows to increase their coating performance in the ultraviolet region.

First of all, welcome to the Microforum, and thank you for your reply. Of course I am considering some applications such as SMLM, but this is a general question about the capability of objective with higher than 1.35-1,4 NA. You are right, but I think using low magnification objective is completely different story. By the way, I am not sure someone uses that expensive 25X water immersion without especial need to long working distance.

Na lensformula

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Yes higher NA can collect more light, but here there is no more incoming light to collect; if you are using other samples ( n1 ) this would be different.

Numerical aperture of objectivelens

Higher NA means higher collection angle by definition. The amount of light collected from an isotropic emitter is proportional to NA^2 (e.g. from an ensemble of randomly oriented fluorophores in fluorescence).

However I think you can get higher resolution, even if you don’t collect more light, because the wavelength of the light will be shorter in the high index media that is used for example by an Olympus 1.7NA. Could this be helpful for PALM/STORM? I think that would depend on what you want to image. I’d say yes if your imaging a sample that is very thin, but maybe no if the sample is thick and you want to image a few microns deep. The distortions due to the refractive index differences are likely to negate any of the gains from the higher NA.

Objective lenses also have transmission curves which tell you how much light gets through. As I understand the main loss mechanism is residual reflections of the AR coatings on internal lens elements (which might be e.g. 1%/surface). It is conceivable that an objective with lower NA but higher transmission might win the competition for collecting the most photons from an identical sample.

Edmund Optics offers all TECHSPEC® transmissive optics with a variety of anti-reflection (AR) coating options that vastly improve the efficiency of the optic by increasing transmission, enhancing contrast, and eliminating ghost images. Most AR coatings are also very durable, with resistance to both physical and environmental damage. For these reasons, the vast majority of transmissive optics include some form of anti-reflection coating. When specifying an AR coating to suit your specific application, you must first be fully aware of the full spectral range of your system. While an AR coating can significantly improve the performance of an optical system, using the coating at wavelengths outside the design wavelength range could potentially decrease the performance of the system.

Anti-reflection V-coats are a type of AR coating designed to increase transmission over a very narrow waveband centered at a specified design wavelength (DWL). This coating type is called “V-coat” because the curve of the transmission versus wavelength forms a “V,” with a minimum at the DWL. V-coats are ideal for obtaining maximum transmission when using single-frequency, small linewidth lasers, or narrow full width-half max (FWHM) light sources.1 V-coats typically have a reflectivity of less than 0.25% at the DWL. However, the reflection curve for the coating locally has a nearly parabolic shape and the reflectivity is significantly higher at wavelengths besides the DWL (Figure 3).

Numerical aperture formula

VIS-NIR: Our visible/near-infrared broadband anti-reflection coating is specially optimized to yield maximum transmission (>99%) in the near-infrared.

VIS 0° and VIS 45°: VIS 0° (for 0° angle of incidence) and VIS 45° (for 45° angle of incidence) provide optimized transmission for 425 – 675nm, reducing average reflection to 0.4% and 0.75% respectively. VIS 0° AR coating is preferred over MgF2 for visible applications.

AR coatings are designed so that the relative phase shift between the beam reflected at the upper and lower boundaries of a thin film is 180°. Destructive interference between the two reflected beams occurs, which cancels out both beams before they exit the surface (Figure 2). The optical thickness of the optical coating must be an odd integer multiple of $\tfrac{\lambda}{4}$, where $ \small{\lambda} $ is the design wavelength or wavelength being optimized for peak performance in order to achieve the desired path difference of $\tfrac{\lambda}{2}$ between the reflected beams. When achieved, this will lead to the cancellation of the beams. The index of refraction of a thin film $ \small{\left( n_f \right)} $ needed for complete cancelation of the reflected beams can be found by using the refractive indices of the incident medium $ \small{\left( n_0 \right)} $ and the substrate $ \small{\left( n_s \right)} $.

HighNA lens

Nice question. An NA higher than the refractive index of your medium will not collect more propagated light. However as you mentioned a NA>n will allow for TIRF/Evanescent wave propagation from your side of the sample, corresponding to high angle propagated light on the imaging and illumination side.

Hi Edalat, My take is same as you here “No, the effective NA can’t be higher than that of the sample media”, unless you are imaging a few hundreds of nm near the coverslip surface.

At this point a strange effect occurs: as the law of light propagation work both ways… you can also collect evanescent light from your sample at such high NA. This is named super critical angle (fluroescence) emission or SAF. In practice this means that fluorophores close to the coverslip will yield more light, but not much will change apart from this.

Numerical aperture of optical fiber

As a final note, I would say to a certain extent you have to try it out yourself to see if a particular objective works in your application. As Hazen said, sometimes you can arrange to test out objectives.

Is this a theoretical question or you have an application in mind? A few other considerations. If you want maximum brightness then aim for low magnification with high NA. Something like the Nikon 25X 1.1NA water immersion is very good for this or a 40X oil immersion. This MicroscopyU article explains more https://www.microscopyu.com/microscopy-basics/image-brightness. Consider refractive index matching to your sample. It may be you are better moving away from oil immersion and to water immersion or silicone immersion (Nikon and Olympus have some very nice options) particularly if you are imaging away from the coverslip. These lenses also have correction collars which correct any spherical aberration.

Some of the high NA TIRF lenses you mention have the disadvantage of not being plan so there is roll off towards the edges of the FOV, but that may not be an issue depending on your desired FOV/detector etc. And of course pixel size is important in the trade-off of resolution and sensitivity/SNR. For PALM/STORM this is usually done with 100X TIRF objectives. Nikon have specialised SR versions with better PSF’s. For the best localisation precisions it’s important to not have aberrations and of course to collect the maximum number of photons per pixel. Depending on the system this is usually a pixel size of 100-160 nm. In this context TIRF illumination helps improve the SNR but my understanding is the this is due to having less out of focus light from the sample rather than improving the light gathering power of the objective. But perhaps someone with a more of an optics background than me can say more on that.

But what you will find in practice is that this setup will deliver brighter images with higher resolution compared to an air objective with NA = 1.0 and similar magnification.

$\tfrac{\lambda}{4}$ MgF2: The simplest AR coating used is $ \tfrac{\lambda}{4} $ MgF2 centered at 550nm (with an index of refraction of 1.38 at 550nm). MgF2 coating is ideal for broadband use though it gives varied results depending upon the glass type involved.

The middle medium with n1=1.3 can be skipped in this theoretical consideration because it only creates a parallel ray offset according to geometrical optics and refraction. [ sin(α1) = 1.0 * sin(α0)/n1 = 1/n1 at α0=90 => sin(α2) = n1 * sin(α1) / n2 = n1/n1/n2 = 1/n2 ]

Table 1 shows the reflectivity and guaranteed laser-induced damage threshold (LIDT) for Edmund Optics’ standard laser V-coats.

Due to Fresnel reflection, as light passes from air through an uncoated glass substrate approximately 4% of the light will be reflected at each interface. This results in a total transmission of only 92% of the incident light, which can be extremely detrimental in many applications (Figure 1). Excess reflected light reduces throughput and can lead to laser-induced damage in laser applications. Anti-reflection (AR) coatings are applied to optical surfaces to increase the throughput of a system and reduce hazards caused by reflections that travel backwards through the system and create ghost images. Back reflections also destabilize laser systems by allowing unwanted light to enter the laser cavity. AR coatings are especially important for systems containing multiple transmitting optical elements. Many low-light systems incorporate AR coated optics to allow for efficient use of light.

Assume a setup with an oil immersion high NA objective with NA = 1.4, n2 = 1.5 and a biological sample with n1 = 1.3 in transillumination with n0 = 1.0 (and NA_ill = 1.0)

Abbe has explained the microscopic image formation based on diffraction occurring due to object structures. According his explanation “…it is the light-gathering power of the objective, which will affect the brightness of the image and its resolution.” Higher NA objectives will gather higher diffraction orders which are emerging at higher angles. The resolution and brightness of an image are increasing with the number of diffraction contributing to image formation. A high NA oil immersion lens will gather diffraction orders in angle directions which are not contained in the illumination.

Different objective lenses have different corrections depending on the target application. Spherical aberrations are the most common type of imaging aberration and occur as you image deeper into a sample that isn’t index-matched with the immersion medium (hence the popularity of silicone oil objectives where the immersion substance better matches the RI of many samples than either water or conventional oil does). Some objective lenses – depending on intended use case and sensitivity to spherical aberration – have correction collars so the user can adjust internal compensation. Some objective lenses have better flat field (plan) correction than others. Some objectives have better chromatic corrections than others (achromat = corrected for 2 colors, fluor = 3 colors, apo = 4 colors). TIRF objectives are usually well-corrected for flatness and chromatically, but multi-photon objectives often do not perform particularly well in either of these categories…