On-Orbit Polarization Calibration for Multichannel Polarimetric Camera

Round 1

Reviewer 1 Report

In this papaer the authors propose a new method for calibrating a polarimetric camera by using the solar light. The theoretical threatment is complemented with an experimental test.

I have three broad comments:

1) some improvement of the introduction is needed. It is some time quite hard to read. I suggest some minor changes in specific points, but a general review is needed.

2) From the introduction it appears that such a method for the calibration of the polarimeter is mainly proposed for detectors dedicated to Earth observation from the space.

I suggest to add some comment on the implications, for a satellite dedicated to Earth observation, to have a "calibration mode" that requires the observation of the Sun.

Can be this operative mode compatible with an Earth observation mission profile? Even if the method is innovative, it should also fit with an Earth observation mission profile for hoping to be implemented actually.

3)The proposed method of calibration is based on the assumption that the observed solar radiation is unpolarized.

Since it is a crucial point I suggest to quantify the limit of polarization admitted to allow this method

still to remain valid with respect to other ones.

The solar radiation has some (small) degree of polarization (the so called "second solar specteum") depending on the center to limb viewing angle and the energy.

See for example "Center-to-limb variation of the second solar spectrum" J.O. Stenflo et al 1997 (Astron. Astrophys. 322, 985–994 (1997)).

If the method you propose is applied on a polarimeter that integrate the disc emission of the sun, for symmetry reasons this polarization cancel out and it is not an issue. But, if only a portion of the solar disc falls in the field of view of the polarimeter the net polarization is not zero (albeit small).

Is it relevant in your calibation method? How can you correct the result for this effect if relevant?

Even if the polarization is negligible, I suggest to mention that you are aware of this issue to remove the doubt of the reader.

p, li { white-space: pre-wrap; }

The specific minor comment are the followings:

line 37: " when the camera works in space, the polarizing effects are changed by the optical structure, material and so on. " The polarizing effect are in general present also on Earth.  Sentence not clear.

line 61: "satellite technical indicators"... "satellite constrains" seems better

line 61: "compromising method"... should be "A method of compromise is the..."

line 74: solar diffuser

line 74: which can be shared with the...

line 80:  is taking..., rotates...

line 81: Are the polarization parameters the Stokes parameters? If yes it is more clear to call them just Stokes parameter.

line 91: polarimetric camera

line 100: You wrote: "Q denotes polarization direction U denotes polarization intensity".

This definition is not clear to me.

I, U and Q is the usual notation of the Stokes parameters.

Q is the intensity difference between polarized components of electromagnetic wave parallel and perpendicular to the reference plane.

U indicates intensity difference between polarized components in planes 45° and −45° to the reference plane.

So, please clarify the meaning of your sentence.

p, li { white-space: pre-wrap; }p, li { white-space: pre-wrap; }

Author Response

Response to Reviewer 1 Comments

 

Dear Editor and Reviewers:

Thank you for your letter and for the reviewer’s comments concerning our manuscript entitled “On-orbit polarization calibration for multichannel polarimetric camera” (ID: 448768). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as following:

Responds to the reviewer’s comments:

Point 1: some improvement of the introduction is needed. It is some time quite hard to read. I suggest some minor changes in specific points, but a general review is needed.

 

Response 1: We have made correction according to the Reviewer’s comments.

We have re-written introduction according to the Reviewer’s suggestion as following:

Polarimetric remote sensing camera is an optical detection system, which is designed for polarimetric imaging of target. It can obtain the degree and the angle of linear polarization, not just the radiance. The polarization information has a multitude of applications in many fields, including agriculture, military reconnaissance, meteorological environment monitoring and other fields [1-3]. At present, most of the detection instruments used for polarization remote sensing are the first-generation polarization detection systems. The types of these systems include the division-of-time (DoT), the division-of-amplitude (DoAM), the division-of-aperture (DoAP) and the division-of-focal plane (DoFP) [4,5]. However, each type has its own weakness, such as the calibration problem of the types of DoAM and DoAP [6], the imaging field of view (IFOV) errors of the type of DoFP [7,8]. However, the polarizing effects caused by the polarimetric camera itself will affect the accuracy of polarization detection. In addition, the polarizing effects are changed by the optical structure, material and so on. For the above reasons, the polarization characteristics of polarized cameras operating in space will be different from those in laboratory calibration. Therefore, the instrument should make the on-orbit polarization calibration at regular intervals to ensure that the detection accuracy is not reduced. This paper intends to provide an on-orbit polarization calibration method for a multichannel polarimetric camera with DoAM. This method has many technological advantages, such as high maturity and stability, wide spectral range, and large field of view.

At present, the commonly used on-orbit calibration methods include the scene calibration, The on-board polarized light source method and the spaceborne linear polarization method. The Polarization and Directionality of the Earth's Reflectance (POLDER) and the Directional Polarized Camera (DPC) has adopted the scene calibration [9,10]. When the polarimetric camera observes the atmosphere in a specific angle, the light reflected by the atmosphere is close to unpolarized light. The camera uses this source as a calibration source for polarization calibration. However, it is hard to meet the requirement of obtaining unpolarized light when observing the atmosphere in reality. Even if the scene calibration method is a simple and easy to operate calibration method, the calibration accuracy is low. The on-board polarized light source method (see Fig. 4) has the highest precision, which is used by the Earth Observing Scanning Polarimeter (EOSP) [11]. The advantage of this method is the polarization calibration can be taken in real time. However, one of the problems of this method is the system lifetime is restricted by the polarized light source. The other problem is that the volume and the power cannot meet the satellite constrains. The spaceborne linear polarization method which has been adopted in Aerosol Polarimetry Sensor (APS) [12]. When the polarimetric camera observes the atmosphere in a specific angle, the on-board polarizer will create polarized light which can be used for the calibration. The accuracy is high enough, and the lifetime of the on-board polarizer is as long as the satellite. The main problem of this method is that the polarizer should cover all fields of view for the optical system, which means that the polarizing plate will be very large. All of the methods above have some inherent problems. Therefore, it is necessary to study a new on-orbit polarization calibration method with high accuracy, small volume and reliable performance.

In this paper, we propose a new on-orbit polarization calibration method, which’s called On-orbit rotating analyzer polarization calibration method. The calibration source is the unpolarized light created by an on-board solar diffuser which can be shared with the on-orbit radiometric calibration. A built-in rotatable linear polarizer (herein, called the linear analyzer) is used to analyze the polarizing effects of the camera. Besides, the built-in linear analyzer can be very small, as it is placed after the optical system. Here we used a micro precision rotation stage to control the linear analyzer rotate precisely. When the polarimetric camera is taking on-orbit solar radiometric calibration, rotates the linear analyzer continuously. The Stokes parameters were calculated by the received radiation intensity. A special model is established for polarization calibration of the polarimetric camera. The proposed method can meet the need of on-orbit polarization calibration with a higher accuracy.

This paper is organized as follows. In Section 2, the main polarization parameters of the camera are analyzed, based on the principle of a multichannel polarimetric camera. In Section 3, the new polarization calibration method is proposed, including the calibration model, on-orbit measurement scheme and the factors acting on the calibration accuracy. Section 4 describes a verification experiment which is conducted to verify the accuracy of the polarization calibration method that this paper proposed. In Section 5, we summarize and conclude the paper.

 

Point 2:

From the introduction it appears that such a method for the calibration of the polarimeter is mainly proposed for detectors dedicated to Earth observation from the space.

1）I suggest to add some comment on the implications, for a satellite dedicated to Earth observation, to have a "calibration mode" that requires the observation of the Sun.

2）Can be this operative mode compatible with an Earth observation mission profile? Even if the method is innovative, it should also fit with an Earth observation mission profile for hoping to be implemented actually.

 

Response 2:

1）It is really true as Reviewer suggested that we should add some comment about the satellite. We have re-written the second paragraph in introduction which shows the commonly used on-orbit calibration methods on satellite.

At present, the commonly used on-orbit calibration methods include the scene calibration, The on-board polarized light source method and the spaceborne linear polarization method. The Polarization and Directionality of the Earth's Reflectance (POLDER) and the Directional Polarized Camera (DPC) has adopted the scene calibration [9,10]. When the polarimetric camera observes the atmosphere in a specific angle, the light reflected by the atmosphere is close to unpolarized light. The camera uses this source as a calibration source for polarization calibration. However, it is hard to meet the requirement of obtaining unpolarized light when observing the atmosphere in reality. Even if the scene calibration method is a simple and easy to operate calibration method, the calibration accuracy is low. The on-board polarized light source method (see Fig. 4) has the highest precision, which is used by the Earth Observing Scanning Polarimeter (EOSP) [11]. The advantage of this method is the polarization calibration can be taken in real time. However, one of the problems of this method is the system lifetime is restricted by the polarized light source. The other problem is that the volume and the power cannot meet the satellite constrains. The spaceborne linear polarization method which has been adopted in Aerosol Polarimetry Sensor (APS) [12]. When the polarimetric camera observes the atmosphere in a specific angle, the on-board polarizer will create polarized light which can be used for the calibration. The accuracy is high enough, and the lifetime of the on-board polarizer is as long as the satellite. The main problem of this method is that the polarizer should cover all fields of view for the optical system, which means that the polarizing plate will be very large. All of the methods above have some inherent problems. Therefore, it is necessary to study a new on-orbit polarization calibration method with high accuracy, small volume and reliable performance.

 

2) This method of calibration is feasible. The method uses the solar diffuser to reflect sunlight as a light source, and detects the deviation by rotating an analyzer placed at the back end of the system. The solar diffuser is shared by the radiometric calibration, so this method does not require an additional light source and is a simple and practical method of in-orbit calibration. In fact, we are developing the satellites that use this calibration method.

 

Point 3: The proposed method of calibration is based on the assumption that the observed solar radiation is unpolarized.

Since it is a crucial point I suggest to quantify the limit of polarization admitted to allow this method still to remain valid with respect to other ones.

The solar radiation has some (small) degree of polarization (the so called "second solar specteum") depending on the center to limb viewing angle and the energy.

See for example "Center-to-limb variation of the second solar spectrum" J.O. Stenflo et al 1997 (Astron. Astrophys. 322, 985–994 (1997)).

If the method you propose is applied on a polarimeter that integrate the disc emission of the sun, for symmetry reasons this polarization cancel out and it is not an issue. But, if only a portion of the solar disc falls in the field of view of the polarimeter the net polarization is not zero (albeit small).

Is it relevant in your calibation method? How can you correct the result for this effect if relevant?

Even if the polarization is negligible, I suggest to mention that you are aware of this issue to remove the doubt of the reader.

 

 

Response 3: The reviewer's comments are very meaningful and thank you very much for your advice. We ignore the tiny polarization characteristics of sunlight. According to the reviewer's help, we read the references. We recognize that this issue does require argumentation. By the reference, we know that the main cause of the second solar spectrum is the uneven distribution of atoms at each sub-level due to the asymmetric radiation field, which is then caused by large angle scattering of the sun's edge. The center-to-limb variation (CLV) obtained from the ZIMPOL I polarimeter system shows that the peak Stokes Q/I is very small and this polarization effect is discontinuous in the spectrum. This has less effect on the calibration accuracy of polarized cameras. Therefore, solar radiation can be regarded as an ideal unpolarized light. We included the article recommended by the reviewer in the reference. And added the corresponding content on line 248 as following:

“…In this work, the accuracy of the polarization calibration mainly depended on the accuracy of the polarization parameters, as the accuracy of the radiometric calibration is high enough using an on-board solar diffuser. Actually， the solar radiation has some degree of polarization which called second solar spectrum. The main cause of the second solar spectrum is the uneven distribution of atoms at each sub-level due to the asymmetric radiation field, which is then caused by large angle scattering of the sun's edge. The center-to-limb variation (CLV) obtained from the ZIMPOL I polarimeter system shows that the peak Stokes Q/I is very small and this polarization effect is discontinuous in the spectrum [22]. This has less effect on the calibration accuracy of polarized cameras. Therefore, solar radiation can be regarded as an ideal unpolarized light.

 

The editorial mistakes have been corrected

 

    We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

    We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval.

    Once again, thank you very much for your comments and suggestions.

 

Reviewer 2 Report

This paper describes novel method of polarimetric camera on-orbit calibration. The method described in the paper is clear and very interesting, but the paper itself is chaotic. Therefore before publications some issues should be addressed:

·       Authors nicely describe different types of polarimetric cameras in the Introduction and section 2.1, then suddenly “the camera” is referred to in section 2.2. This specific camera is not introduced earlier. Separate section generally describing cameras and sections about specific camera should be clearly separated, otherwise reader do not have a clear picture and can be confused.  

·       Statements in the paragraph between lines 134-137 should be justified and possibly quantitatively assessed

·       The statement starting in line 165 should be supported by at least one additional sentance.

·       Line 172 what analyzer is referred to when authors write “this analyzer”?

·       In analysis result of the relative deviation of the radiance intensity between an ideal lambertian source and an actual aluminium solar diffuser some justification of used values is needed (lines 290-291).

·       Line 299: should be Fig. 8.

·       The statement about the 2% accuracy of the method is not addressed further in the text

Additionally the paper contains large number of editorial mistakes, e.g.:

·       Lack of spaces after punctuation marks

·       Lack of subscripts and superscripts, e.g. lines 148, 279, 280

·       Formulas not fitting in lines, e.g. lines 223, 224, 279

·       In lines 342 and 343 “in this paper” is repeated

Author Response

Response to Reviewer 2 Comments

 

Dear Editor and Reviewers:

Thank you for your letter and for the reviewer’s comments concerning our manuscript entitled “On-orbit polarization calibration for multichannel polarimetric camera” (ID: 448768). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as following:

Responds to the reviewer’s comments:

 

Point 1: Authors nicely describe different types of polarimetric cameras in the Introduction and section 2.1, then suddenly “the camera” is referred to in section 2.2. This specific camera is not introduced earlier. Separate section generally describing cameras and sections about specific camera should be clearly separated, otherwise reader do not have a clear picture and can be confused.

 

Response 1: We have made correction according to the Reviewer’s comments. Section 2.1 shows the measurement method for the polarization information on partially linear polarized light and the real-time multi-channel polarization camera. The specific camera we mentioned in section 2.2 is the same as the real-time multi-channel polarization camera in section 2.1. We are very sorry for our negligence of expression which may make reader feel confused. We have re-written the lines 105-110 according to the Reviewer’s suggestion as following:

 

Since the method above needs to rotate the analyzer three times, the measurement cannot be updated in real time. Therefore, we propose a multi-channel polarization camera that enables real-time shooting. Three fixed analyzers with three polarization axis angles, which are 0°, 60°, and 120°, are proposed to measure the polarization information simultaneously. The schematic of the multichannel polarimetric camera is shown in Fig. 2（a）. Optical design model of the multichannel polarimetric camera is illustrated in Fig. 2（b）. The image of target is caught by the pre-optical system. The collimating lens transforms the imaging light into parallel light. The parallel light is separated into three channels by two beam splitters located in the rear of the collimating lens.

 

Point 2: Statements in the paragraph between lines 134-137 should be justified and possibly quantitatively assessed

 

Response 2: It is really true as Reviewer suggested that the Statements in the paragraph between lines 134-137 should be justified. We have added corresponding references which is” L. C. Chen, F. G. Meng, Y. L. Yuan, X. B. Zheng. Experimental study for the polarization characteristics of airborne polarization camera [J]. Journal of Optoelectronics. Laser ,2011,22(11):1629-1632.”

We have re-written the lines 133-137 according to the Reviewer’s suggestion as following:

 

As we known, the polarizing effects are related to the optical structure, material, wavelength, aperture and coating [13]. In this multichannel polarimetric camera, the collimating lens, the beam splitters and the converging lens can be designed and optimized into approximately unpolarized elements, because their diameters and aperture angles are small. [14] The degree of polarization of the optics decreases as the angle of view decreases. At a 670 nm channel, an optical component with a field of view of 0.3 rad has a degree of polarization lower than 0.01. That means we should consider the polarizing effects of pre-optical system and the linear analyzers.

 

Point 3: The statement starting in line 165 should be supported by at least one additional sentence.

 

Response 3: We have added data support and re-written the paragraph as following:

 

Fig. 3 (b) shows that the polarization state of the exit light is partially linear polarized light. We can see from Fig. 3 (c) and (d) that the diattenuation ε₁ and the retardance are changed according to the field of view and the wavelength. The parameters rise as the increase of the field of view. Their changes as the wavelength are decided by the material or the coating of the mirrors. For the material of aluminum, the diattenuation ε₁ at 870 nm is larger than the other wavelength. On the contrary, the retardance at 870 nm is smaller than the other wavelength. From the figures above we can see that the maximum polarization degree ε₁ for this system is up to 2%. and the biggest phase retardance for this system is less than 0.005°. In this case, the influence of the diattenuation ε₁ for this system cannot be ignored, and the phase retardance for this system can be ignored, which can be indicated by Fig. 3.

 

Point 4: Line 172 what analyzer is referred to when authors write “this analyzer”?

 

Response 4: We are very sorry for our negligence of the Category of the analyser. We chose THORLABS' Wire Grid Polarizers on Glass Substrates as a reference.

 Line 172, “But the extinction ratio of this analyzer（Wire Grid Polarizers on Glass Substrates, WP25M-UB, THORLABS） is not high enough, because it is usually made up of wire grid for large acceptance angle.” was added

 

Point 5: In analysis result of the relative deviation of the radiance intensity between an ideal Lambertian source and an actual Aluminium solar diffuser some justification of used values is needed (lines 290-291).

 

Response 5: It is really true as Reviewer suggested that We should explain why the ideal Lambertian source cannot be achieved.

We have re-written the lines 297-300 according to the Reviewer’s suggestion as following:

 

the polarization degree of the solar diffuser as DoLP₀=0-4%. In the development process of this instrument, the physical production process has been optimized by physical grinding and chemical etching. However, there is still no guarantee that the roughness is consistent with the ideal Lambertian body, which leads to the polarization effect. The analysis result of the relative deviation δ(DoLP₀) is shown in Fig. 7.

 

Point 6: The statement about the 2% accuracy of the method is not addressed further in the text

 

Response 6: We are very sorry for our incorrect writing” The accuracy of this method is at least 2%.”. The statements were corrected as “At 670nm channel, the instrument measurement accuracy can reach 0.8% after calibration by this method”

 

The editorial mistakes have been corrected

 

    We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

    We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval.

    Once again, thank you very much for your comments and suggestions.

 

.

Round 2

Reviewer 2 Report

The paper is nicely and clearly written, I recommend it for publication. However I suggest a few minor corrections:

Lines 62-63: “The spaceborne linear polarization method which has been adopted in Aerosol Polarimetry Sensor (APS) [12]” – something is missing in this sentence.

Line 139: "polarizing" should start with capital letter

Lines 149, 182, 247: strangely looking comma is written

Lines 292-301: The paragraph, after adding the clarification into it is not well written. I suggest changing the order of sentences, by putting newly added sentences (“In the development … polarization effect”) at the beginning of the paragraph (line 293), after “solar diffuser from Eq. (15)”   

Author Response

Response to Reviewer Comments (round 2)

 

Dear Editor and Reviewers:

Thank you very much for your E-mail of Mar. 15 regarding the submission of our manuscript entitled “On-orbit polarization calibration for multichannel polarimetric camera”.

We would like to thank reviewer for their encouragement and comments. We have implemented all the concerns suggested by the reviewers. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as following:

 

Point 1: Lines 62-63: “The spaceborne linear polarization method which has been adopted in Aerosol Polarimetry Sensor (APS) [12]” – something is missing in this sentence.

 

Response 1: We are very sorry for our negligence of the missing sentence. We have re-written the lines 62-63 according to the Reviewer’s suggestion as following:

The spaceborne linear polarization method which has been adopted in Aerosol Polarimetry Sensor (APS) can solve the above problems [12].

 

Point 2: Line 139: "polarizing" should start with capital letter

 

Response 2: We are very sorry for our incorrect writing about the "polarizing". We have modified this format error.

 

Point 3: Lines 149, 182, 247: strangely looking comma is written

 

Response 3: We are very sorry for our incorrect writing about the comma. We have modified this editing error.

 

Point 4: Lines 292-301: The paragraph, after adding the clarification into it is not well written. I suggest changing the order of sentences, by putting newly added sentences (“In the development … polarization effect”) at the beginning of the paragraph (line 293), after “solar diffuser from Eq. (15)”

 

Response 4: It is really true as Reviewer suggested that the paragraph is not well written. We should introduce the reasons for the formation of non-ideal Lambert bodies at first, and then carry out numerical analysis. We have re-written the lines 292-301 according to the Reviewer’s suggestion as following:

We can analyze the relative deviation of the radiance intensity between an ideal Lambertian source and an actual aluminium solar diffuser from Eq. (15). In the development process of this instrument, the physical production process has been optimized by physical grinding and chemical etching. However, there is still no guarantee that the roughness is consistent with the ideal Lambertian body, which leads to the polarization effect. Here, we assume the angle of linear polarization of the diattenuation for the optical system as θ₁=30°, the polarization angle of the solar diffuser as σ₀=60°, the polarizer axis angle of the linear analyzer as θ’=20°, the range of the extinction ratio as E_i=0-1/100, the range of the diattenuation of the optical system as ε₁=0-10%, and the range of the polarization degree of the solar diffuser as DoLP₀=0-4%. The analysis result of the relative deviation δ(DoLP₀) is shown in Fig. 7.

 

We are sorry for the carelessness. We have checked the revised manuscript and corrected some other mistakes.

 

We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your carefulness and responsibility.

 

Yours sincerely.

Xin Zhang.

Author Response File: Author Response.pdf