Preamble

Vol. 66 No. 5

September 2025

Acta Astronomica Sinica

Analysis of Narrow-band Optical Imaging Observations for MASTA and WFST Wide-field Telescopes

XU Xiao¹,², LOU Zheng¹,², PING Yi-ding¹,², DONG Yun-fen¹,²,³, ZHENG Xian-zhong¹,²,⁴†

¹ Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023
² School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026
³ CAS Nanjing Astronomical Instruments Co., LTD, Nanjing 210042
⁴ Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210

Abstract

In optical systems with small focal ratios, the performance of narrow-band filters is significantly affected by the telescope's optical configuration and the angle of incident light. From the center to the edge of the field of view, the increasing deflection of the incident angle causes a blue shift in the central wavelength, broadening of the bandpass, and attenuation of the maximum transmittance for narrow-band filters. To address the requirements for narrow-band survey observations with WFST (Wide Field Survey Telescope) and MASTA (Multi-Application Survey Telescope Array), we quantitatively analyze how the central wavelength and bandpass of different narrow-band filters vary with the field radius.

WFST has a focal ratio of 2.49 and a maximum off-axis incident angle of 13.27°. At maximum deflection, narrow-band filters with central wavelengths of 395 nm and 656 nm exhibit a maximum central wavelength blue shift of 0.78 nm. The 10 nm and 1 nm bandpasses increase by 2.67% and 41.80%, respectively, while the maximum transmittance attenuation coefficients are 80.00% and 74.50%. MASTA has a focal ratio of 1.74 and a maximum off-axis incident angle of 18.48°. At maximum deflection, the central wavelengths at 395 nm and 656 nm blue shift by 2.70 nm. The broadening of the 10 nm and 1 nm bandpasses reaches 4.20% and 81.70%, respectively, with maximum transmittance attenuation coefficients of 80.00% and 63.90%. Future narrow-band observations of emission or absorption lines with WFST and MASTA must systematically account for the effects of central wavelength blue shift and bandpass broadening.

Keywords: telescopes, instrumentation: filters, techniques: photometers, wide-field imaging

1 Introduction

Narrow-band surveys, which utilize narrow-band filters to target specific emission lines, are widely applied in astronomical research. Compared to spectroscopic observations, narrow-band photometry can efficiently measure the intensity of target emission lines for numerous objects across wide fields, enabling effective selection of specific emission-line sources. Additionally, the sky background in the optical bands corresponding to these filters is typically lower, facilitating the detection of fainter emission-line signals. Currently, several telescopes worldwide equipped with wide-field cameras have endowed optical narrow-band surveys with powerful observational capabilities.

For observations within the Milky Way and nearby galaxies, narrow-band imaging enables studies of emission-line nebulae, including the spatial distribution of H II regions, planetary nebulae, Herbig-Haro (H-H) objects, and supernova remnants. Investigating these emission-line nebulae provides rich information about star formation and evolution. For instance, H II regions effectively trace star-forming regions, and since ionized gas often exhibits strong Hα emission, photometric measurements of this line serve as a primary method for detecting both local and global star formation in galaxies. Planetary nebulae are commonly identified through strong [O III] doublet and Hα lines, with the MASH (The Macquarie/AAO/Strasbourg Hα Planetary Nebula Catalogue) providing numerous samples for subsequent studies [1]. H-H objects can be identified by combining [S II] and Hα lines, tracing outflows near young stars and indicating active star formation [2–4]. Supernova remnants reflect the properties of their progenitor stars. Since supernova explosions occur on very short timescales, observations of the explosions alone cannot fully characterize the final stages of stellar evolution. Supernova remnants help complete our understanding of stellar evolution and can constrain the physical properties of any central compact objects [5–6].

Narrow-band observations also efficiently identify and confirm emission-line galaxies at medium to high redshifts. Based on sufficiently large samples of emission-line galaxies, valuable galaxy parameters such as emission-line luminosity functions can be obtained. Galaxy luminosity functions are commonly fitted using the Schechter function [7], which describes the distribution of galaxy numbers within specified luminosity intervals. The luminosity function provides information about the environment of galaxy samples, such as whether they reside in clusters or general fields, and the distribution of different galaxy types within the sample [8–11]. When telescope resolution is insufficient to resolve galaxy morphology, the luminosity function can constrain galaxy types. Connecting luminosity functions with other galaxy characteristic functions yields additional insights; for example, comparing them with stellar mass functions can reveal relationships between stellar mass and star formation rate within given redshift ranges [12–13]. Different emission lines vary in dust absorption intensity and production mechanisms, and comparing these differences provides richer information than single emission lines alone. For instance, comparing Lyα and Hα luminosity functions can analyze galaxy dust structure and morphological feature distributions [14–15]. Galaxy parameters evolve with redshift, and comparing luminosity functions of the same emission-line galaxy type at different redshifts reveals how stellar population characteristics change with cosmic evolution [16–18].

Many characteristic emission lines are crucial for studying high-redshift galaxies, with the Lyα emission line being particularly representative as the strongest emission line. Since Partridge and Peebles [19] first highlighted the importance of Lyα emission lines for high-redshift galaxy studies, numerous observational investigations have been conducted [20–22]. Early emission-line studies were limited by telescope capabilities, constrained by small apertures and fields of view, yielding results for only small regions and limited samples. This limitation motivated the development of large-aperture, wide-field telescopes. In recent years, the construction of large-aperture, wide-field telescopes has significantly expanded the depth and breadth of emission-line research. Large apertures ensure high-sensitivity detection of faint signals, while wide fields enable systematic observations of large-scale structures and large samples, advancing emission-line studies considerably. During the cosmic noon period at redshifts z ≈ 2–3, when Lyα emission lines from celestial objects redshift into the visible band, optical narrow-band filters can be used to detect emission sources. This era, characterized by rapid formation of massive galaxies and cosmic structures with peak cosmic star formation and AGN activity, is ideal for studying galaxy evolution in relation to cosmic environment. Large samples of emission-line galaxies can reveal the large-scale structure of protoclusters and predict their future evolution [23–26]. Additionally, extended structures with Lyα emission, known as Lyα blobs/nebulae, effectively trace ionized intergalactic medium, and their distribution can map the structural characteristics of intergalactic medium in galaxy clusters, which trace the evolution of cosmic large-scale structures [27]. For the reionization epoch (z > 6), Lyα emission lines also provide rich scientific information. Since Lyα photons are easily resonantly scattered by neutral hydrogen, this emission effectively traces the ionization state of neutral interstellar medium during reionization [28].

Similar to Lyα, Hα emission lines can also be used to identify high-redshift galaxies [29] and trace star formation rates. For example, the HiZELS (The High-z Hα Emission Line Survey) [30] has provided numerous Hα luminosity functions and star formation rates for emission-line galaxies at different redshifts.

Combined with the observational capabilities of new-generation wide-field survey telescopes, a series of narrow-band observation projects have been or are planned to be conducted. Some observations targeting objects within the Galaxy and nearby galaxies focus on star formation and evolution, spatially resolved distributions of star-forming regions, planetary nebulae, and stellar population properties of globular clusters, such as S-PLUS (The Southern Photometric Local Universe Survey) [31] and BNBIS (The Byurakan Narrow Band Imaging Survey) [3–4]. Other observation programs targeting medium to high-redshift galaxies focus on luminosity function evolution of different emission lines, differences in galaxy properties across environments, protocluster structures, and their correlation with dark matter halos, such as SILVERRUSH (Systematic Identification of LAEs for Visible Exploration and Reionization Research Using Subaru HSC) [32], SFACT (The Star Formation Across Cosmic Time) [33], and ODIN (The One-hundred-deg² DECam Imaging in Narrowbands) [34]. Wide-field survey facilities can provide vast amounts of observational data; for example, HSC with its 1.7° diameter field of view can obtain nearly 1 TB of data per night. New-generation survey telescopes such as LSST (The Large Synoptic Survey Telescope), Roman (The Nancy Grace Roman Space Telescope), and the Wide Field Survey Telescope (WFST) designed by Purple Mountain Observatory have larger fields of view and higher observational efficiency. Taking WFST as an example, this telescope has a 2.5 m aperture, a focal ratio of 2.49, and a 3° diameter field of view. Its ongoing survey plans can cover approximately 8000 deg² for wide-field observations and 1000 deg² for high-frequency deep fields, reaching limiting magnitudes about 2 mag deeper than SDSS (Sloan Digital Sky Survey) within a 6-year planned observation period. One advantage of wide fields is more efficient and comprehensive monitoring of time-domain signals, such as AGN variability, tidal disruption events (TDEs), and supernova explosions. Another advantage is the ability to conduct deep observations of large-scale structures and matter distributions; stacked wide-field data can better enable cosmological studies such as gravitational lensing and galaxy cluster formation [35–37].

Due to emission-line contributions, strong emission-line targets exhibit significantly higher measured fluxes in narrow-band observations than in broadband observations, meaning high-redshift emission-line galaxies can be discovered through narrow-band imaging. However, in most cases, the bandpass of such filters is wider than the typical line width of emission lines, and the filter transmittance varies considerably across the bandpass, leading to substantial uncertainties in redshift and flux derived from observations with a specific narrow-band filter [38]. To address this issue, more accurate redshift and flux estimates can be determined from flux ratios observed through different narrow-band filters and several matching broadband filters.

Particularly in optical systems with large focal ratios, narrow-band imaging is significantly affected by the telescope's optical system and the angle of incident light. In this study, we analyze how optical performance parameters of narrow-band filters vary with field angle for two wide-field telescopes—WFST and MASTA (Multi-Application Survey Telescope Array)—using the blue-end 395 nm and r-band 656 nm narrow-bands as examples, providing quantitative results to support future narrow-band observations.

2 Principles of Narrow-band Filters

Table 1 lists several commonly used narrow-band wavelengths and their corresponding emission lines and observational targets. Narrow-band observations are also frequently used to identify emission-line galaxies within specific redshift ranges, such as Lyα emission-line galaxies. The table also lists the corresponding Lyα redshift values for several bands.

[TABLE:1]

Currently, most widely used narrow-band filters are based on all-dielectric filters, which are multi-layer Fabry-Pérot interferometers with each layer thickness being an integer multiple of one-quarter the central wavelength [39]. This type of narrow-band filter can be equivalently modeled as a sandwich structure with two interfaces [40–41], making calculations of transmittance and bandpass parameters more straightforward.

For all-dielectric filters, the wavelength of maximum transmittance satisfies:

$$2n d \cos\theta = m\lambda \quad (1)$$

where $n$ is the refractive index of the spacer layer, $\theta$ is the effective incident angle, $d$ is the thickness of the spacer layer, $\lambda$ is the wavelength of incident light, and $m$ is a positive integer. According to Snell's law, if the refractive index outside the filter equals 1, then $n\sin\theta = \sin\theta_0$, where $\theta_0$ is the incident angle of the incoming light.

The relationship between central wavelength shift $\Delta\lambda$ and incident angle $\theta$ satisfies [42]:

$$\Delta\lambda = \lambda - \lambda_0 = \lambda_0\sqrt{1 - \frac{\sin^2\theta}{n^2}} - \lambda_0 \simeq -\frac{\lambda_0\sin^2\theta}{2n^2} \simeq -\frac{\lambda_0\theta^2}{2n^2} \quad \text{if } \theta \ll 1 \quad (2)$$

where $\lambda_0$ refers to the original central wavelength.

In actual telescope optical systems, the beam incident on the filter is not parallel light at a fixed angle but rather a converging beam with a half-angle $\theta$ (related to the system's focal ratio) that illuminates the focal plane. Consequently, each point on the focal plane integrates light from a range of incident angles. Analysis must therefore be based on the imaging beam characteristics of the optical system. Assuming the filter is placed in this converging light path with its surface normal (or optical axis) perpendicular to the filter plane, and the beam's half-aperture angle is $\theta$, the relationship between bandpass width variation and incident angle under these conditions can be described by:

$$\frac{\Delta\lambda}{\Delta\lambda_0} = (1 + X^{1/2}) \quad \text{where } X = \frac{F}{B^2} \quad (3)$$

where $\Delta\lambda$ is the filter's actual bandpass when the incident light is a converging beam with half-angle $\theta$, $\Delta\lambda_0$ is the ideal bandpass for perfectly parallel incident light, and $F$ is a parameter related to specific coating parameters. Detailed calculation methods for parameter $F$ can be found in the work of Lissberger et al. [40–41].

When light is incident at an angle, its optical path length within the coating layers increases, causing the filter's peak transmittance to decrease. In practical optical systems, the chief rays from central and edge regions of the focal plane have different incident angles relative to the system optical axis. Oblique incidence results in effective optical path lengths within each coating layer that are significantly greater than the physical thickness, with different incident angles corresponding to different effective path length increments. These combined optical path effects ultimately cause a blue shift in the filter's central wavelength and broaden and distort its transmission spectrum.

The above analysis and formulas for bandpass variation apply to parallel (collimated) beams with specific incident angles. However, in real telescope systems, each image point on the focal plane represents the integrated result of light across its corresponding range of incident angles. [FIGURE:1] shows the range of incident light angles for each image point on the focal plane. Notably, the distributions of incident angle ranges for image points at the field center and edge differ subtly, covering all possible incident angle magnitudes. Therefore, reliable results must be calculated based on the actual range of incident angle variations to determine changes in filter optical performance (such as bandpass width and central wavelength). Furthermore, while the central wavelength shift formula above addresses single incident angles, for image points in actual converging beams (which encompass a range of incident angles), the relationship must be integrated to obtain the effective optical performance of the filter at that image point.

Equation (3) calculates the coefficient for narrow-band filter bandpass variation. For a specific point on the focal plane, the integrated average over the angular range must be computed. Referring to equation (4), using the telescope's optical system parameters, one can calculate the range of incident angles on the filter for light converging to image points on the focal plane, including both on-axis and off-axis points:

$$\Delta\lambda = \int_{\theta_1}^{\theta_2} [1 + X(\theta)^{1/2}] \Delta\lambda_0 \, d\theta / \Delta\theta \quad (4)$$

where $\Delta\theta = \theta_2 - \theta_1$.

The deflection of incident angles affects filter transmittance, bandpass width, and central wavelength. Following the methods of Lissberger et al. [40–41] and Zheng et al. [42], we simulated the optical parameters of filters under different incident angle offsets.

The filter's central wavelength shifts toward the blue as the angle of incidence (AOI) increases. This shift depends only on the original central wavelength and incident angle magnitude, independent of bandpass characteristics. [FIGURE:2] shows how the central wavelength shift varies with incident angle for filters with different central wavelengths.

[FIGURE:3] compares the bandpass variation characteristics of 1 nm and 10 nm bandpass filters under changing parallel light incident angles. Bandpass width shows low sensitivity to incident angle changes, with observable variations only at large incident angles and extremely narrow original bandpasses (1 nm), where increasing incident angle causes slight broadening. Peak transmittance attenuation correlates with both original central wavelength and original bandpass—longer wavelengths and narrower bandpasses experience greater attenuation.

3.1 WFST Narrow-band Optical Performance

WFST is a wide-field survey telescope designed and built for large-scale surveys. The telescope's optical configuration is described in Lou et al. [43], and its main specifications are listed in Table 2.

[TABLE:2]

WFST has a primary mirror aperture of 2.5 m and a focal ratio of 2.49. In its optical system, the maximum incident angle deviation at the field edge is 13.27°, whose effects cannot be ignored. For two cases with central wavelengths (CWL) of 395 nm and 656 nm, we adopt filters with bandpasses of 10 nm and 1 nm (i.e., 395 nm/10 nm, 656 nm/1 nm). [FIGURE:4] shows the simulated transmittance variations of these filters under collimated light conditions at different incident angles, extending from the field center to the field edge. Here, the filter bandpass is defined as the full width at half maximum (FWHM) of the simulated transmittance curve.

3.2 MASTA Narrow-band Optical Performance

The Multi-Application Survey Telescope Array (MASTA) is primarily used for searching and discovering large quantities of medium- and high-orbit space debris. Table 3 provides the main specifications for a single telescope in the array.

[TABLE:3]

This telescope has an aperture of 710 mm, a focal length of 1238 mm, and a focal ratio of 1.74. Compared to WFST, MASTA exhibits larger incident angle deflections at the field edge, with a maximum off-axis incident angle deviation of 18.48°. For the same two central wavelength cases (395 nm and 656 nm) with 10 nm and 1 nm bandpass filters (395 nm/10 nm, 656 nm/1 nm), [FIGURE:5] shows the simulated transmittance variations under collimated light conditions at different incident angles from the field center to the field edge.

The angular ranges of converging beams for on-axis and off-axis positions and the corresponding bandpass variation coefficients for both optical systems are shown in Table 4, while Table 5 presents the relationship between blue-end shift of the central wavelength and incident light angle.

WFST's focal ratio is 2.49 with a maximum off-axis incident angle of 13.27°. At maximum deflection, narrow-band filters with central wavelengths of 395 nm and 656 nm exhibit a blue shift of 0.78 nm. The 10 nm and 1 nm bandpasses broaden by 2.67% and 41.80%, respectively, with maximum transmittance attenuation coefficients of 80.00% and 74.50%. MASTA has a focal ratio of 1.74 and a maximum off-axis incident angle of 18.48°. At maximum deflection, the central wavelengths at 395 nm and 656 nm blue shift by 2.70 nm. The 10 nm and 1 nm bandpasses broaden by 4.20% and 81.70%, respectively, with maximum transmittance attenuation coefficients of 80.00% and 63.90%.

Since on-axis and off-axis positions encompass all possible light incident angles, the range of bandpass variation for narrow-band filters in both telescopes can be determined. For WFST, filters with an original 10 nm bandpass will not exceed 2.67% variation after changes; those with an original 1 nm bandpass will not exceed 41.80% variation. For MASTA, filters with an original 10 nm bandpass will not exceed 4.17% variation; those with an original 1 nm bandpass will not exceed 81.70% variation.

3.3 Impact of Narrow-band Filter Optical Performance Changes

Based on the simulation calculations for narrow-band filters in both telescope systems, we can estimate deviations in redshift measurements when observing and confirming high-redshift targets. Taking Lyα emission-line galaxies as observational targets, a filter with a central wavelength of 395 nm would normally identify target galaxies at redshift z ≈ 2.24. In WFST, the maximum wavelength blue shift of 0.78 nm would shift the target redshift to 2.22, corresponding to a distance reduction of 26.5 Mpc. In MASTA, the maximum blue shift of 2.70 nm would shift the target redshift to 2.16, reducing the distance by 107.6 Mpc.

According to the analytical relationship between filter central wavelength shift and light incident angle, the shift magnitude $\Delta\lambda$ strictly depends on the optical system's focal ratio and the filter medium's refractive index $n$ (which together determine the maximum half-angle $\theta_{max}$). Consequently, the observed target redshift offset $\Delta z$, which is related to the central wavelength, is also completely determined by these parameters.

Taking a Lyα emission source at z = 2.24 as an example: when observed with a narrow-band filter centered at 395 nm, the theoretical detection wavelength is $\lambda_{obs} = 399.8$ nm. [FIGURE:6] quantitatively shows how measured redshift values vary with incident angle. The results demonstrate that telescopes with smaller focal ratios exhibit larger observed redshift offsets.

If this narrow-band filter is used to observe targets with an original redshift estimate of 2.24 without correction, the combined effects of central wavelength shift, bandpass broadening, and peak transmittance attenuation will significantly distort the observational results. [FIGURE:7] shows the transmittance curves of wide and narrow-band filters along with the simulated spectral energy distribution (SED) of an emission-line source. It clearly illustrates that the shifted filter transmission curve no longer matches the emission-line profile, causing the target signal to fall outside the effective bandpass coverage.

Comparing differences between broadband and narrow-band photometric data for the same target is a common method for identifying emission-line objects. When narrow-band filter transmittance curves shift and broaden, the excess of narrow-band photometric values relative to broadband values decreases significantly, reducing the signal-to-noise ratio of photometric observations. By convolving the simulated filter transmittance curves with the target's energy spectrum, the relative flux magnitudes of wide and narrow-band photometry can be obtained as follows:

$$L_{relative} = \frac{\int \phi_{filter}(\lambda) \cdot \phi_{target}(\lambda) \, d\lambda}{\int \phi_{filter}(\lambda) \, d\lambda} \quad (5)$$

where $\phi_{filter}$ and $\phi_{target}$ refer to the filter's transmittance curve and the target's spectral energy distribution, respectively.

We selected simulated broadband filter data covering 395 nm with a 150 nm bandpass and compared it with narrow-band photometry results before and after offset. The results show that for a 10 nm bandpass, 395 nm filter installed on MASTA, the relative photometric flux is 204.05, decreasing to 197.30 after transmittance curve offset, while the broadband relative photometric flux is 180.04. This demonstrates that narrow-band photometry results are affected.

As incident angle increases, the filter's central wavelength experiences a blue shift while peak transmittance decreases, causing mismatch between the target spectrum and the filter's nominal response and reducing effective signal strength. Additionally, oblique incidence increases filter reflection losses and scattering noise, further degrading signal-to-noise ratio. Taking a 656 nm filter as an example and assuming a target magnitude of 20, we calculated signal-to-noise ratio variations using WFST telescope and camera parameters. This calculation was completed using the DECam exposure time calculator with new moon sky background conditions. When the incident angle increases from 0° to 18°, the filter's peak transmittance decreases by approximately 20.0%, corresponding to a signal-to-noise ratio reduction of about 21.7%. This effect is particularly significant in wide-field photometry, requiring angle-dependent correction factors in observation planning and data processing to compensate for signal-to-noise ratio losses and ensure consistent data quality. Table 6 shows how narrow-band observation signal-to-noise ratio changes with increasing incident angle.

[TABLE:6]

Combining signal-to-noise ratio degradation with photometric flux measurement bias, and referring to the general process for identifying emission-line galaxies, we estimated the proportion of targets that might be misidentified as false sources. Following the criteria from An et al. [13], we used the following standard to select emission-line galaxy sources:

$$(m_{NB} - m_{BB}) > \sigma \sqrt{\sigma_{NB}^2 + \sigma_{BB}^2}, \quad EW > 50\text{Å} \quad (6)$$

where $m_{NB}$ and $m_{BB}$ represent narrow-band and broadband photometric magnitudes, respectively, while $\sigma_{NB}$ and $\sigma_{BB}$ are the background sky noise in narrow-band and broadband observations. The parameter $\sigma$ ranges from 2 to 3, and $EW$ refers to the emission-line equivalent width derived from flux differences. The measurement results of $EW$ are influenced by sample selection criteria; different color selections or narrow/broadband threshold settings lead to variations in the obtained $EW$ distribution. This equivalent width selection criterion converts to a magnitude difference of $(BB - NB)_{EW=50\text{Å}} = 0.77$.

Based on this criterion, we used Monte Carlo methods to simulate broadband and narrow-band photometric data for 1000 emission-line sources, calculating the proportion of successfully identified sources before and after accounting for signal-to-noise ratio and photometric flux effects. In this criterion, the affected parameters are narrow-band photometric magnitude $m_{NB}$ and background sky noise term $\sigma_{NB}$. We plotted color-magnitude diagrams for selecting emission-line sources before and after parameter changes, shown in [FIGURE:8] and [FIGURE:9], which mark the proportion of identified emission-line sources relative to all sources.

[FIGURE:8]
[FIGURE:9]

The simulation results demonstrate that the susceptibility of narrow-band filters to incident angle variations leads to signal-to-noise ratio degradation and offsets in narrow-band photometric magnitudes, reducing identification rates when actually confirming emission-line galaxies and significantly decreasing sample identification accuracy.

Overall, the combined effects of central wavelength blue shift and bandpass broadening substantially degrade the observational quality of emission-line objects. Bandpass broadening directly increases the dispersion of redshift measurements for emission-line objects, significantly weakening the statistical reliability of galaxy cluster membership identification. Meanwhile, the blue-shifted central wavelength, combined with the broadened bandpass, introduces stronger continuum noise from the sky background, causing systematic selection bias in emission-line galaxy samples.

4 Summary

We have analyzed and presented the variation of narrow-band filter transmittance parameters with light incident angle from the field center to the edge for the WFST and MASTA telescope optical systems. WFST has a focal ratio of 2.49 and a maximum off-axis incident angle of 13.27°. At maximum deflection, narrow-band filters with central wavelengths of 395 nm and 656 nm exhibit a maximum central wavelength blue shift of 0.78 nm. The 10 nm and 1 nm bandpasses broaden by 2.67% and 41.80%, respectively, with maximum transmittance attenuation of 80.00% and 74.50%. MASTA has a focal ratio of 1.74 and a maximum off-axis incident angle of 18.48°. At maximum deflection, the central wavelengths at 395 nm and 656 nm blue shift by 2.70 nm. The 10 nm and 1 nm bandpasses broaden by 4.20% and 81.70%, respectively, with maximum transmittance attenuation coefficients of 80.00% and 63.90%.

Based on these results, WFST's incident angle deflection has minimal impact on filter optical performance when using 10 nm narrow-band filters. Only when target sources have relatively long central wavelengths might the blue shift of the central wavelength produce perceptible effects. Due to its smaller focal ratio, MASTA exhibits significantly larger central wavelength shifts than WFST under the same conditions, so precision will be more noticeably affected when observing narrow-band targets, such as when using broadband-narrowband flux differences to identify emission-line galaxies. For 1 nm bandpass narrow-band filters, transmittance attenuation and bandpass broadening are much more pronounced, meaning ultra-narrow-band filters are more severely affected.

During actual filter production and installation, the final transmittance curve can be adjusted through coating design, such as appropriately shifting the designed bandpass range toward the red end. This means making the filter's target central wavelength longer and the target bandpass narrower during the design phase, so that the actual optical performance better matches the design requirements.

Acknowledgments

We thank the reviewers for their valuable suggestions, which significantly improved the quality of this paper. We acknowledge the assistance from the ADS database and data support from the WFST team.

References

Miszalski B, Parker Q A, Acker A, et al. MNRAS, 2008, 384: 525
Strom K M, Strom S E, Wolff S C, et al. ApJS, 1986, 62: 39
Movsessian T, Magakian T, Reipurth B, et al. MNRAS, 2024, 530: 2068
López R, Riera A, Estalella R, et al. A&A, 2021, 648: A104
González-Díaz R, Galbany L, Kangas T, et al. A&A, 2024, 684: A104
Suherli J, Safi-Harb S, Seitenzahl I R, et al. MNRAS, 2024, 527: 9263
Schechter P. ApJ, 1976, 203: 297
Binggeli B, Sandage A, Tammann G A. ARA&A, 1988, 26: 509
Binggeli B, Tarenghi M, Sandage A. A&A, 1990, 228: 65
Bremnes T, Binggeli B, Prugniel P. A&AS, 1998, 129: 313
Bremnes T, Binggeli B, Prugniel P. A&AS, 1999, 137: 337
Yan L, McCarthy P J, Freudling W, et al. ApJ, 1999, 519: L47
An F X, Zheng X Z, Wang W H, et al. ApJ, 2014, 784: 93
Song M, Finkelstein S L, Gebhardt K, et al. ApJ, 2014, 791: 3
Lilly S J, Tresse L, Hammer F, et al. ApJ, 1995, 455: 108
Blanc G A, Adams J J, Gebhardt K, et al. ApJ, 2011, 736: 31
Torralba-Torregrosa A, Gurung-López S, Arnalte-Mur P, et al. A&A, 2023, 680: A14
Partridge R B, Peebles P J E. ApJ, 1967, 147: 868
Hu E M, McMahon R G. Nature, 1996, 382: 231
Cowie L L, Hu E M. AJ, 1998, 115: 1319
Rhoads J E, Malhotra S, Dey A, et al. ApJ, 2000, 545: L85
Geach J E, Sobral D, Hickox R C, et al. MNRAS, 2012, 426: 679
Ouchi M, Ono Y, Shibuya T. ARA&A, 2020, 58: 617
Wen R, An F X, Zheng X Z, et al. ApJ, 2022, 933: 50
Harikane Y, Ono Y, Ouchi M, et al. ApJS, 2022, 259: 20
McCarthy P J, Spinrad H, Djorgovski S, et al. ApJ, 1987, 319: L39
Konno A, Ouchi M, Ono Y, et al. ApJ, 2014, 797: 16
Bunker A J, Warren S J, Hewett P C, et al. MNRAS, 1995, 273: 513
Sobral D, Smail I, Best P N, et al. MNRAS, 2013, 428: 1128
Mendes de Oliveira C, Ribeiro T, Schoenell W, et al. MNRAS, 2019, 489: 241
Shibuya T, Ouchi M, Konno A, et al. PASJ, 2018, 70: S15
Sieben J, Carr D J, Salzer J J, et al. AJ, 2023, 166: 101
Lee K S, Gawiser E, Park C, et al. ApJ, 2024, 962: 36
Wang T G, Liu G L, Cai Z Y, et al. SCPMA, 2023, 66: 219502
Liu Z Y, Lin Z Y, Yu J M, et al. ApJ, 2023, 947: 59
Lei L, Zhu Q F, Kong X, et al. RAA, 2023, 23: 035013
Zabl J, Freudling W, Møller P, et al. A&A, 2016, 590: A120
Battaini F, Ragazzoni R, Antonino P M, et al. Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation V, 2022, 12188: 721
Lissberger P H. JOSA, 1959, 49: 121
Lissberger P H, Wilcock W L. JOSA, 1959, 49: 126
Zheng Z Y, James E R, Wang J X, et al. PASP, 2019, 131: 074502
Lou Z, Liang M, Yao D Z, et al. SPIE, 2016, 10154: 587